{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "vaqi-1F39kAh"
},
"source": [
"# **TD1**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "s53win6Y9vTf"
},
"source": [
"## **Exercice 1**\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "j9612ruY95w4"
},
"source": [
"### 1.Create a Data Frame\n",
" "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "P9nysFR_-g0B",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"ourdata <- data.frame(\n",
" x= c(18, 7, 14, 31, 21, 5, 11, 16, 26, 29),\n",
" y= c(55, 17, 36, 85, 62, 18, 33, 41, 63, 87)\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Gt6lbhdIBjTc"
},
"source": [
"### 2.Display the Data"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 429
},
"id": "POHwxfRNBpgT",
"outputId": "4dc06116-8a1f-4084-ee39-9292d1134a6a",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 10 × 2\n",
"\n",
"\t| x | y |
|---|
\n",
"\t| <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| 18 | 55 |
\n",
"\t| 7 | 17 |
\n",
"\t| 14 | 36 |
\n",
"\t| 31 | 85 |
\n",
"\t| 21 | 62 |
\n",
"\t| 5 | 18 |
\n",
"\t| 11 | 33 |
\n",
"\t| 16 | 41 |
\n",
"\t| 26 | 63 |
\n",
"\t| 29 | 87 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 10 × 2\n",
"\\begin{tabular}{ll}\n",
" x & y\\\\\n",
" & \\\\\n",
"\\hline\n",
"\t 18 & 55\\\\\n",
"\t 7 & 17\\\\\n",
"\t 14 & 36\\\\\n",
"\t 31 & 85\\\\\n",
"\t 21 & 62\\\\\n",
"\t 5 & 18\\\\\n",
"\t 11 & 33\\\\\n",
"\t 16 & 41\\\\\n",
"\t 26 & 63\\\\\n",
"\t 29 & 87\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 10 × 2\n",
"\n",
"| x <dbl> | y <dbl> |\n",
"|---|---|\n",
"| 18 | 55 |\n",
"| 7 | 17 |\n",
"| 14 | 36 |\n",
"| 31 | 85 |\n",
"| 21 | 62 |\n",
"| 5 | 18 |\n",
"| 11 | 33 |\n",
"| 16 | 41 |\n",
"| 26 | 63 |\n",
"| 29 | 87 |\n",
"\n"
],
"text/plain": [
" x y \n",
"1 18 55\n",
"2 7 17\n",
"3 14 36\n",
"4 31 85\n",
"5 21 62\n",
"6 5 18\n",
"7 11 33\n",
"8 16 41\n",
"9 26 63\n",
"10 29 87"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ourdata"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "QRM-l30zB6kM"
},
"source": [
"### 3.Plot the Data"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "d_PH9yj1CA2O",
"outputId": "5397bf7c-23a9-4c72-eab0-5869d487a2f6",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
"Plot with title “Scatter Plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(ourdata$x, ourdata$y, xlab='Independent Variable(x)', ylab = 'Dependent Variable(y)', main = 'Scatter Plot')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "CGfsz44MPe5O"
},
"source": [
" ***Looking at this diagram, can we suspect\n",
"a linear relationship between these two variables?***\n",
"\n",
"---\n",
"\n",
"\n",
"\n",
"Yes, based on the scatter diagram, we can suspect a linear relationship between these two variables. The points in the scatter diagram roughly follow a straight line, suggesting that there is a linear trend between the variables x and y. The visual alignment of the points along a straight line indicates a potential linear association between the two variables."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "mJ7LPtNaQkMe"
},
"source": [
"### 4.Fit a Linear Model"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 329
},
"id": "YaZiKfYOQxBs",
"outputId": "cba262ca-044c-4db1-e2f5-2eba7eac420d",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = y ~ x, data = ourdata)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-9.1250 -3.2721 0.5488 3.4878 6.6707 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 1.0213 3.7915 0.269 0.794 \n",
"x 2.7348 0.1922 14.226 5.81e-07 ***\n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 5.164 on 8 degrees of freedom\n",
"Multiple R-squared: 0.962,\tAdjusted R-squared: 0.9572 \n",
"F-statistic: 202.4 on 1 and 8 DF, p-value: 5.807e-07\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"model <- lm(y~x, data = ourdata)\n",
"summary(model)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-Srxjrm5RVFY"
},
"source": [
"### 5.Get the Coefficients (Slope & Intercept)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "lTmKmAKuRg_x",
"outputId": "9c1609f8-6de8-4a3e-f04e-5d89065e25cc",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Slope: 2.734756 \n",
"Intercept: 1.021341"
]
}
],
"source": [
"slope <- model$coefficients[2]\n",
"Intercept <- model$coefficients[1]\n",
"cat('Slope: ', slope, '\\n')\n",
"cat('Intercept: ',Intercept )"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "wqqHJ1Wfbh39"
},
"source": [
"### 6.Get the ordinates of the 𝑦*i* (y-hat)i"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 52
},
"id": "Dq7BlxKrb4Fb",
"outputId": "726ca6eb-14f1-4ab4-bce3-470761aefd77",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"- 1
- 50.2469512195122
- 2
- 20.1646341463415
- 3
- 39.3079268292683
- 4
- 85.7987804878049
- 5
- 58.4512195121951
- 6
- 14.6951219512195
- 7
- 31.1036585365854
- 8
- 44.7774390243902
- 9
- 72.125
- 10
- 80.3292682926829
\n"
],
"text/latex": [
"\\begin{description*}\n",
"\\item[1] 50.2469512195122\n",
"\\item[2] 20.1646341463415\n",
"\\item[3] 39.3079268292683\n",
"\\item[4] 85.7987804878049\n",
"\\item[5] 58.4512195121951\n",
"\\item[6] 14.6951219512195\n",
"\\item[7] 31.1036585365854\n",
"\\item[8] 44.7774390243902\n",
"\\item[9] 72.125\n",
"\\item[10] 80.3292682926829\n",
"\\end{description*}\n"
],
"text/markdown": [
"1\n",
": 50.24695121951222\n",
": 20.16463414634153\n",
": 39.30792682926834\n",
": 85.79878048780495\n",
": 58.45121951219516\n",
": 14.69512195121957\n",
": 31.10365853658548\n",
": 44.77743902439029\n",
": 72.12510\n",
": 80.3292682926829\n",
"\n"
],
"text/plain": [
" 1 2 3 4 5 6 7 8 \n",
"50.24695 20.16463 39.30793 85.79878 58.45122 14.69512 31.10366 44.77744 \n",
" 9 10 \n",
"72.12500 80.32927 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ordinates <- model$fitted.values\n",
"ordinates"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ops5_AdjcdfW"
},
"source": [
"### 7.Visualization of the regression line"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "SM8RoAVvcmec",
"outputId": "fe274f0f-6bba-4d93-8391-6633f9d8530b",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Plot with title “Linear Regression Model”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"#Scatter Plot with The 'best-fit line'\n",
"plot(ourdata$x, ourdata$y, xlab='Independent Variable(x)', ylab = 'Dependent Variable(y)', main = 'Linear Regression Model', col='blue')\n",
"abline(a=Intercept, b=slope, col='red')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "gEzFQhVjeCol"
},
"source": [
"### 8.Make Predictions"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"id": "CyrDukgReWmE",
"outputId": "9eeba381-4fda-411b-f85e-2fc1a46778b7",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"1: 58.4512195121951"
],
"text/latex": [
"\\textbf{1:} 58.4512195121951"
],
"text/markdown": [
"**1:** 58.4512195121951"
],
"text/plain": [
" 1 \n",
"58.45122 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Estimate of y for xi = 21\n",
"predict(model, newdata = data.frame(x = c(21)))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "12V8XHsgpZyM"
},
"source": [
"***Does the least squares line obtained in question 3 pass through point (xi\n",
", yi\n",
") ? Can we generalize this conclusion to any regression line?***\n",
"\n",
"---\n",
"\n",
"\n",
"\n",
"The linear regression line goal is to best estimate y for a given x, but it does not gurantee to pass through the points exactly. In practice, due to random variability and measurement errors, observed points might not exactly lie on the least squares line, but the line is chosen to minimize the overall error."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Z2vuDrujpysZ"
},
"source": [
"## **Exercice 2**\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "zYzNx7tasUJx"
},
"source": [
"### 1.Create a Data Frame\n",
" "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 429
},
"id": "fXgoMNElsLIc",
"outputId": "db25cf56-2f3a-46f2-d7fc-7617985908d0",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 10 × 2\n",
"\n",
"\t| x | y |
|---|
\n",
"\t| <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| 0.2 | 19 |
\n",
"\t| 0.2 | 21 |
\n",
"\t| 0.4 | 35 |
\n",
"\t| 0.4 | 38 |
\n",
"\t| 0.6 | 64 |
\n",
"\t| 0.6 | 66 |
\n",
"\t| 0.8 | 115 |
\n",
"\t| 0.8 | 130 |
\n",
"\t| 1.0 | 200 |
\n",
"\t| 1.0 | 210 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 10 × 2\n",
"\\begin{tabular}{ll}\n",
" x & y\\\\\n",
" & \\\\\n",
"\\hline\n",
"\t 0.2 & 19\\\\\n",
"\t 0.2 & 21\\\\\n",
"\t 0.4 & 35\\\\\n",
"\t 0.4 & 38\\\\\n",
"\t 0.6 & 64\\\\\n",
"\t 0.6 & 66\\\\\n",
"\t 0.8 & 115\\\\\n",
"\t 0.8 & 130\\\\\n",
"\t 1.0 & 200\\\\\n",
"\t 1.0 & 210\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 10 × 2\n",
"\n",
"| x <dbl> | y <dbl> |\n",
"|---|---|\n",
"| 0.2 | 19 |\n",
"| 0.2 | 21 |\n",
"| 0.4 | 35 |\n",
"| 0.4 | 38 |\n",
"| 0.6 | 64 |\n",
"| 0.6 | 66 |\n",
"| 0.8 | 115 |\n",
"| 0.8 | 130 |\n",
"| 1.0 | 200 |\n",
"| 1.0 | 210 |\n",
"\n"
],
"text/plain": [
" x y \n",
"1 0.2 19\n",
"2 0.2 21\n",
"3 0.4 35\n",
"4 0.4 38\n",
"5 0.6 64\n",
"6 0.6 66\n",
"7 0.8 115\n",
"8 0.8 130\n",
"9 1.0 200\n",
"10 1.0 210"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Given Data\n",
"ourdata <- data.frame(\n",
" x= c(0.2, 0.2, 0.4, 0.4, 0.6, 0.6, 0.8, 0.8, 1.0, 1.0),\n",
" y= c(19, 21, 35, 38, 64, 66, 115, 130, 200, 210)\n",
")\n",
"#Print the Data\n",
"ourdata"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "lmW33WGra_O8"
},
"source": [
"### 2.Plot the Data"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "1kvbb-BUavPh"
},
"source": [
"***Does a linear adjustment seem justified? What coefficient should you calculate with R?***\n",
"\n",
"---\n",
"\n",
"\n",
"\n",
"To determine if a linear adjustment is justified, we can create a scatter plot of the data and visually inspect whether the points roughly form a straight line."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "YHra-hsqbIOs",
"outputId": "d5895a3d-5822-447a-d762-83152d550bb6",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"image/png": 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XQ7pjpfV1fiPzl7vu78RakZCgGVdDCmype1llXXb1uSrvkxgrEhI0435IHfI2mV8X+66KsSIhQTOuh7RH3RxYHtby+Gvf31DhZkKCXlwPaZt6IrA8zX/clZ/4VIQDdf0egBdcD6k0rzCwXHDy8dceLK4wl2ck6MXdkEasL9p7U/tvzcXNJ1wSY0X+RoJm3A3JtsgwnjwhbV2MFQkJmnE1pIX3zZw4eljfFYYxr+VLsVYkJGjGo08ROlgW82pCgmY8+ziufUUxriQkaMazkKbGuhdCgmYICRDgPKTPlj89/+nln9X2TggJycRhSFuvax/cpt1+Qg1vjTB1j9CckJBEHIW0pyBDNRs+7f7H7582vKnKKNhTww3T0rIqpBMSkoiTkN5olj5qY3nwTPnGUenNVsW+4dTc8KY6frVDMnESkr9P5fcUFfU5fkfU4xzr2uNYaJmQkEychDT9+A8wKZ1ewy035dwQWiQkJBOnW+3Omf91bW76zVehpVWFMVYjJGjGaUgZKmfE/8Xe36cOCAmacRrSvof7pav8W2Lt71MHhATNCOzZsOeP56epH/9J8j2thATNyOwitOO+zqrBr7dIDBRASNCMSEiHn78iR7X2+28tr2r1OiAkaEYgpDd/eaLKGfWGse0KNVNmKEKCbpyGtO3ODkp1fXC/tVzev5nQVIQEzTgNKU3l/XpD6MyDPomRDEKCdpyG1Puxw+EzRUucDxRASNCMk5A2RF0TfUndEBI04ySkzPuPu+L+WAdYrg1CgmachHSt6vVqxMWv9lLjRWYiJGjH0d9ITzVWHSe++MGukl0fvDixo2r8lNRUhATNONvYcLDwlIqPvW9+t9yDn5CgGadb7crWFRZc2vfSgsL1kruAExI049nHccVESNCMQEgHPtgvNEwFQoJmHIe0qrtSywzjkr+LjWQQErTjNKS3M3MHmCHtaZ4p9WKshZCgGachDW69faf1jLS79VC5oQgJunEaUuNCIxCSMauR2EyEBO04/vCTvwZDWljDZ9rVCiFBM05DanVLMKSr2kiNZBAStOM0pF812miFVHyzGic3FCFBN05D2pmf0U116ZKlWu+SG4qQoBvHryPtvqaxUqrJNbvFRjIICdoR2LOhfFeR5LORhZCgGSchba9McCpCgmachKQqE5yKkKAZJyENr0xwKkKCZngbBSBAIKRtq5ev2Sk0ThAhQTOOQ3qkXeAPpE7PiI1kEBK04zSkB1Xm+WOvG3tepnpMbihCgm6chtThe/8NnG4/vZPQRBZCgmachuSfGVy4J0tinCBCgmachtQidEzlP7YUmcdGSNCM05B+0zv4MVyXTpYZKICQoBmnuwhtHXzeU+9//tELlwyQ/CghQoJm2EUIiWPvggkTFuz1eoo6kdtFiA8/gUNP57a67LJWuU97PUddiO0idEhy5wZCSkWrMuaYf3CXzc74h9eT1IFYSE+e6niWMEJKRX3G2qcF53k6Rt04DmnvA5Mnmq5umSs2EyGlpMNpq+yFN9JLvJ2kLpyG9FnT4KaGjNvkhiKkVPSl2mIvbFFfejtJXTgNaVTugyvUn167seVrcjMRUkoqyVhhL/w944i3k9SF05Ba32iUqLWG8c7Jb8oNRUgpqf8o+3Rkf2/nqBPH+9otMO/C2soyvZ/YTISUmtZmTj9qGEemZ/7L60nqwGlIJ99hGA0XmgtP50mNZBBSinqpceN+/Ro3ecnrOerCaUhDW75h9OphPuz/t5ncUISUog48O23aswe8nqJOHB8fKbu78ajKv6yLGiU3FCFBN45fR9rwkFF+U47yXSq5ixQhQTMyezaUfHZYYpgKhATNOAlpZ7H5vzDBqQgJmnH0NooBld5KITgVIUEzjt5GUVjprRSCUxESNMMnrQICnIa09AO5WcIICZpxGlL23XKzhBESNOM0pP4Dy+SGqUBI0IzTkHaNuPipDUUBckMREnTjNCQ2fwOG85CGX1kwNkhuKEKCbvgUIUAAnyIECOBThAABfIoQIIBPEQIE8ClCgAA+RQgQwKcIAQL4FCFAAJ8iBAhwFNI+g08RAiyOQsoaGTwQB58ihBTnKKR8pc64d5/oPDZCgmYchVS27CeZKmuU/JEKCQmacbqxYd99PzCfluZ+JTeRhZCgGYG9v9ddnaeyR/1TaKAAQoJmRN5GcfiJARmqo8g8NkKCZoTej7R3Vg5vNUcKkwjp6PMXp6v8mSLz2AgJmnEe0vvXN1HpQ/5WKjWRhZCgGYchfbOgp1KtZm4XnMhCSNCMo5D+OaaBShu8VPTJKICQUtP+v/z2t3/Z7/UUdeIoJKVaztgmOk4QIaWkxSedMnDgKSct9nqOunAU0qB6eDIKIKRU9Kb/zu8M47s7/ZJvtnYLh3VBojh/tH36i/M9HaNuCAkJoiR9pb2wMr3E20nqgpCQIL5UW+yFLepLbyepC0JCgihJf8Ne4BlJDCGlIv5GEkdIqSilt9qtDr0T6e1FIvPYCCklLT6p+aCUfB3JWn4huHBPI5F5bISUmlJ1z4aiZcvUjGUBS85uIDgVIUEzjkIqjDjwpfqJ4FSEBM04+9Vux1J1ZWHA7EXHBKciJGjG6d9Ig9fKzRJGSNAMm78BAU5DKn9uSJczbXJDERJ04zSkOUo1yLPJDUVI0I3TkFoN2Co3TAVCgmYcH7HvX3KzhBESNOP4GYmtdoDzkKaMk5sljJCgGachHRww8rVNRQFyQxESdON4p9UwuaEICbpxGtKI0WND5IYiJOiGPRsAAQIhHfhA/B0khATNOA5pVXellhnGJX8XG8kgJGjHaUhvZ+YOMEPa0zxzg9xQhATdOH4bRevtO61npN2th8oNRUjQjdOQGhcagZCMWXxmA1KY05Ay/hoMaaFfbCZCgnYc72t3SzCkq9pIjWQQErTjNKRfNdpohVR8s5Lc6Y6QoBmnIe3Mz+imunTJUq13xXXb8q3LlyxZUdPRyQgJmnH8OtLuaxorpZpcszueWxZPbmbvl9f69sOx1iMkaEZgz4byXUXxPRsZO9qpDmNmzp49bUQL1bk4xoqEBM24uq/dWP9zwaXSeb6JMVYkJGjGSUg9K+la8w2bF4SXh+fHWJGQoBknIaVb/OZfPD7zf3mxwgjy3xVevjUzxoqEBM04/dWuuPf4d0uMA2/+7IKva75hm5+Gl4e2jbEiIUEzTkMqCLUxOI439k30zTliLx2aoabGWJGQoBmnITX9c3BhTtOab7i/m8rtN+ba8aP7NlC9Y6VCSNCM05Cy7g4u3JgVz3eb2yXdehnJf86C0ljrERI04zSkri3XBU7fbtY5vhuXfLxxY9HRGlYiJGjGaUgvp6v2F15yYXvle67a9SOxixCSkuMXZFcPzDZ/V8vs+1o8t2QXISQpgT0byr74ePt3cd2QXYSQrNhFCBDg6oHGYu8itGNrhTsJCXpx9UBjMXcR+sQXeYx0QoJWXD3QWOxdhLbxjARtuXqgMXYRQrJy9UBj7CKEZOXugcbYRQhJyvUDjbGLEJKRZwca2xcrPEKCZjw70NjUWOEREjTj2YHGCAnJxLMDjRESkomrBxrrHqE5ISGJuHqgsbS0rArphIQk4uqBxqbmhjfV8asdkomrBxo71rXHsdAyISGZuHugsU05N4QWCQnJxOUDjX3zVWhpVWGM1QgJmuFAY4AAtw80Fh9CgmbcPdBYvAgJmnH1QGNxIyRoRiCkHf9e+d4eoXGCCAmacRzSgraB91Cc8bTYSAYhQTtOQ3pIZfUfPW7U2T71F7mhCAm6cRrS9wfYBxj7tH0noYkshATNOA0p883gwrx4DusSL0KCZhwfaCz0KULzW4rME7wzQoJeHB/68ubgwpBJIvPYCAmacRrSjrNH/m3z55sWDepftN0kNBUhQTOCnyJU+08SqhYhQTNOQxo2vBKhqQgJmvHsU4RiIiRoxrNPEYqJkKAZVz9FKG6EBM24+ilCcSMkaMbVTxGKGyFBM65+ilDcCAmacfdThOJFSNCMy58iFCdCgmb4FCFAAJ8iBAjgU4QAAXyKECDAcUgfP37P758XfToyCAnacRjS2+cE3j3hGxrnMc3jREjQjLOQXstW3W568L7xbVXeW5JTERI04yik/c0aPB9YKH3Qf8rXckMREnTjKKT71KOhxQfVLKGJLIQEzTgKqX+rstBiWeueQhNZCAmacRTSKSPCF47OE5nHRkjQjKOQ/L8JXzhF8g3ohATNOApJTQ1fGPOYsLVFSNAMIQECnIV07swK5xISUpizkOrjwyEthATNOArpiUoEpyIkaIYPiAQEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJBSyZFlc+YsO+L1FEmJkFLIylYNevRo0Gql13MkI0JKHe/kTDB/rAcm5Lzj9SRJiJBSx6DL7dPLBnk7R1IipJRxxP+6vfC6/6i3kyQjQkoZX6ot9sIW9aW3kyQjQkoZ36atPvr6nDmvH/1n2rdez5J8CCl19Bqan9O9e07+0F5eT5KECCl1zFMXHDCMA+erh7yeJAkRUuoY1DWr45gxHbO7stVOHiGljCP+1z+/Z8yYOZ+/lslWO3GElDLYalefCCllfOtbbS+w1a4eEFLq6DXePh3PVjt5hJQ6lmU8Yp0syHjN60mSECGlkIezOl11Vaesh72eIxkRUir5fM7o0XM+93qKpERIgABCAgQQEiCAkAABhAQIICRAACEBAggJEEBIgABCAgQQEiCAkAABhAQIICRAACEBAggJEEBIgABCAgQQEiCAkAABhAQIICRAACEBAggJEEBIgABCAgS4HVL51uVLlqzYVsNahATNuBtS8eRmKqD17YdjrUdI0IyrIe1opzqMmTl79rQRLVTn4hgrEhI042pIY/3PBZdK5/kmxliRkKAZV0NqXhBeHp4fY0VCgmZcDcl/V3j51swYKxISNONqSG1+Gl4e2jbGioQEzbga0kTfnCP20qEZamqMFQkJmnE1pP3dVG6/MdeOH923geodKxVCgmbcfR3p6Nwu6dbLSP5zFpTGWo+QoBnXdxEq+XjjxqKjVVyx1a8iHHLyPQC3ebGv3dF1Kz+NvrT8zeUVfq+qSg1IWK6GdMdK6+v8RuYzTvd3Yq24hpCgF1dDCmype1llXXb1uSrvkxgrEhI0435IHfI2mV8X+66KsSIhQTOuh7RH3RxYHtYyxoqEBM24HtI29URgeZo/xoqEBM24HlJpXmFgueDkGCsSEjTjbkgj1hftvan9t+bi5hMuibEiIUEz7oZkW2QYT56Qti7GioQEzbga0sL7Zk4cPazvCsOY1/KlWCsSEjTj0acIHSyLeTUhQTOJ+XFchATNEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQkqXT1/PmrYx75CUmKkASt7ZBxxhkZHdZ6PQfcR0hyPmg4dp9h7CvI/dDrSeA6QpIzdHC5dVI+eKjXk8B1hCTmaNar9sKrWce8nQTuIyQxX6ot9sJHaoe3k8B9hCTmkO8te2GNj0NJpxxCkvOjSfbppB95Owc8QEhylvqfsk6ezFjq9SRwHSEJui+jY9++HTPu83oOuI+QBP2rra9hQ1/bt72eA+4jJDkf5l611zD2XpW7yetJ4DpCkjNskP2C7MBhXk8C1xGSmIoXZF/hBdnUQ0hiKl6Q3cILsqmHkMTwgmwqIyQ5Pa63T6/v4e0c8AAhyXnR/4x18rT/Ra8ngesISdC9GT0nTOiZMdfrOeA+QpK0efrll0/f7PUU8AAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECNArpLL1CxeuL6v3bw/UllYhbTjT17at78wN9f79gVrSKaSP8kbtNIydo/I+qvcBgNrRKaTLB5RbJ+UXXV7vAwC1o1FIx7Jfthdezj5W7xMAtaJRSDvUFnvhI7Wj3icAakWjkA761pZteOyxDWVv+Q7V+wRArWgUktHtyrNU27bqrCu71fsAQO3oFNL9qre11a63eqDeBwBqR6eQLu+Q3vuGG36c3uGKeh8AqB2NQjqW/fJ/bhw8+Mb/vMRWOyQajUJiqx0Sl0YhHVRr7QW22iHhaBSS0W2KfXoDW+2QaHQK6fnMJdbJksxF9T4AUDs6hWQUpveZMqVPemG9f3+glrQKyXhv6qBBU9+r928P1JZeIQEJipAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIgIDFDWq8Azayv9cO8/kMy3t1QjYv7PJHQ+jCfIwk/38XVPTLfrf2j3IWQqjVmjIffPA7M50xKzUdI1WM+Z1JqPkKqHvM5k1LzEVL1mM+ZlJqPkKrHfM6k1HyEVD3mcyal5iOk6jGfMyk1HyFVj/mcSan5CKl6zOdMSs1HSNVjPmdSaj4vQ/rVrzz85nFgPmdSaj4vQyou9vCbx4H5nEmp+bwMCUgahAQIICRAACEBAggJEEBIgABCAgQQEiCAkAABhAQIICRAACEBAggJEEBIgABCAgQQEiDA9ZD2T2zjP3XsjvAFxZNbZ7YdutbtOaoTNZ/lejXWm2miRc/3ap+Geee/4dU8x4uab/PPm2c0Gfa2dxMd59iNad0jz1f5H7z23A7paDd1xV0F/nYVb078qq0aPH1URvZ/XB6kGlHzWdanJ0xI0fM9qk6bdkPTzNof0adeRM33Qe7JMx6/o3nGCi+nirCpW26lkKr8D14Hboc0V/3O/Pqsmhy6YLx6wPy6WA1yeZBqRM1n+q5L54QJKYcNtl8AAAlHSURBVGq+3Q27HjKMoobjPBwqQtR8I9VK8+t7qq93M0X6JqdHUVZkSFX9B68Lt0PqknvEOmnfrDx4waR+x8yv5TltXB6kGlHzme72LUuYkKLmm6Nes07Kq72Fu6Lm66ms/77GiW09G6mSryYfMyqFVNV/8LpwOaSS9H6B0zFqa6XLj/jPdXeQalQ13yc51+xPlJCi5xuQc8w48o13E1UWPd9o9b75dW/aQM9mihIZUnUPyFpzOaSPlf1ZYjPV8kqX/yHwC573qpqv36lfJ0xI0fO16fTvc33qtIWejVRJ9HybGnVevfPf/Rr8y7uhjhcZUnUPyFpzOaSNanzgdI5aEnnxqswff+fuINWoYr6FapGRMCFFz5fb5tTJi/7QWj3p3VARqvj5fdRJKdX6Lc9GihYZUjUPyNpzPaRrA6ez1QsRlz6V1e0rd+eoTvR8u08eYiRSSMfPl6X+Yn7d0bB5qWdDRYieb1O7/Htf+vOZeQ7/wZdUOaSqHpB14HJIRWp04HSa+nvFZeUz1MUH3B2jWtHz/azh5wkUUvR8jdO/tU7+RyXE6wfR853T4Avz67ctWx7zaqYokSFV9YCsE5dDOpphbwYdoT4PXVReoK5LiH9NLVHzvaqmb9++/UM1YntC/EEf/fPrnh54hI5TCfFCUtR8B33nB05/oT7waqYokSFV8YCsG7c3f/dsYP0DWtYiv+KSiWqWyzPEcvx8k1XIVC/HqhD187tWBf6Mv0ht82ymSMfPt0f1Cpz+VG3wbKbjVdr8Hf2ArBu3Q1qgbjW//lHdZhgl73xiWC/FTnR5hJiOn2/TS5Zn1EUvbfZ6tICon98G3wVHDGN92g+9nswWNV87/xbz6/6TTzzi8WRhwZDs+SIGdsTtkEp7q6G3/cz3A/OfgfeVtQn/NHXd1IDE+MT1qPkCEuZvpCrmm6S63Pa/OZlveDxYUNR8S9Ia3/LoXe3UPK8ns60yH2npzc0v+4LzRQzsiOs7rR68oY2/5XhrI539f6TiV6fP3J6kasfPF5A4IUXPVz6/c3beoHUej1Uhar63hjXNaNT/FY/HCikMPdyKQvOFB3aEt1EAAggJEEBIgABCAgQQEiCAkAABhAQIICRAACEBAggJEEBIgABCAgQQEiCAkAABhAQIICRAACEBAggJEEBIgABCAgQQEiCAkAABhAQIICRAACEBAggJEEBIgABCAgQQEiCAkAABhAQIICRAACEBAgjJPek93bxZJcPVzspnt1exGDQ+M+K4ydP9q5x/91RASPI2qwFVXi4fUmFRaGmQWh1cKsvP2he94oBKh+iNFdJT6v6Ic6V9mu2pzbApi5DkuRbSDrUstLhUjQkuLVMja7zLGCEdbHxOpfNF6QXxjZniCEmeayEtDYdU2vKEA/bST1TNv4zFCOluddxxk0dmfBrfnKmNkOTZIY1QB3/bJrPV3HJz+ZVu2U3H7g8UsWtca3+TodZByIepHWObZZ7+kFHp0hpvFl5hsHV07tBvdDPUgsDpvszTDePtYY39bX7+mWF1srt/9lL7b6TIS7f+pkXm6fOMYEjhey9rfob5dblvhHVfA9PMe9+gJrj0c9MaIcmzQxqtBvx67ZqL1KOG8WZ6i1mP/Ly33yxiT5u8qU/MapW1ynoInz11zeoL1SOVLq3xZuEV1l6pZrwQOq79tjT7ies+da+xIbvF7QtuzG1m/q10pRo5cNb7gZAiLh2uBveeNeN71re2Qoq49/V2Nr9Wyw1jkbreXCxv2t6bH6NeCEmeHdJYZf2rvlUNMf9lV9Y/9uOU+VC/JmO9ubgtt4f1ELZW+DqrbaVLa7xZxAqF4V/tDPP56QPr5AdZ+4yHur1hLj2gHjCMAnVRmWFvtYu4dLjqbV7638x2dkgR916oXrTu5WDbDkcO5X//sBG47Wcu/NB0R0jyQiG9Zp1p0MUoyznNWnrHLKK8SbedlgHqoPkAXWpd3F/tiLy0xpuFV6gc0tLA88c6Nco+e6xkhZpsTfGkdS60+Tt46XD70vPVNiukyHsvsHM0Vvpm3pD2VmBxmvXshBoQkrxQSJusM3lnGl+oC62lErOIXSrkQ/MhvNm6eLT6d+SlNd4svELlkEpbNTlqGFerf5jLj/c5yVp5ojVF4EWhQEjhS4er943AiKutkCLv/VK1y767cVn+KfbS/erp+v6JJQFCkhcKKfAij/mA/1hdErjc19MoUl2W2fabD+HPrUvHqZWRl9Z4s/AKlUMyZqrnjcN51raCm1SPhavW/skOKbC2FVLEpcFvfZ35XGOGFHnvfVWJfW8blR2b2Z+aX68/ruRASPKOD2m7/dRyMPDU0qViteH2U8so9V7kpTXerNqQtqdfbDyh5prPYTn5B83zr1UOKfLS4eoj+67W2M9I4XsPPSOV9Tqlce/ywCLPSPEgJHnHh/RdZmC71xprq0GT7P3WsrW3wHC12Fo8W+2JvLTGm1UbkjEkfe+A7K8M4zN1mXX2psohRV46XL1gLfc1n6esjQ0R915g/npnmaOeWah+H1iczt9IcSAkeceHZD5grc1vIwOb39TN5uKe5kMC26DNxS2+0ytdWuPNIlaYrZZEft+/qVkZ1qaGw76u5td3WqqrI0OKvHR44LfG7ZmdglvtwvdeaG8B2ZIzyDDOb/CxtfwzttrFgZDkRYX0qq/ZjXOGXJBnFrG7tbrqsVmt/f9nPYT7D5n/UFtrA1rEpTXeLGKFRerse9eFv29pfo76p7UwRF399PRGr2a0eupQxN9IEZcOVxcNe/i+jtbvbFZIEfe+znrCMn+xO+G/Zk1Z55YZRnkzXkeKAyHJiwrJeOYHmU0L9udbTwk7r8nPOOnStw3rIVw0qUVmp8eMSpfWeLOIFY5dkdPo+YhvfKvqGDjdM7Jp3gWrjdsaNt8ZEVLEpUNV8aRTMzsuNIJ7NoTvvewU6y7usf7UMozb1b3WVofr6vfHlRwIyTPRb2BIBIXq1coXjMrY6s0keiEkzyRmSAcb96p0/hP2/o4LIXkmMUPi/Uh1Q0ieSdCQjGsrv0P2Dc8G0QohAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASICA/w9nxgC5GUdqUQAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title “Scatter Plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"#Draw the scatter Plot\n",
"plot(ourdata$x, ourdata$y, xlab='Independent Variable(x)', ylab='Dependent Variable(y)', main='Scatter Plot')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9r66W44ycnCa"
},
"source": [
"### 3.Correlation Coefficient (r)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LsS-DbOZcxTk"
},
"source": [
"Additionally, we can calculate the correlation coefficient (r) to quantify the strength and direction of the linear relationship between the two variables."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"id": "yIFiBY5NbZvU",
"outputId": "a80094a0-d0d1-4b0e-862c-e07b1fcccfc4",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"0.955955936345808"
],
"text/latex": [
"0.955955936345808"
],
"text/markdown": [
"0.955955936345808"
],
"text/plain": [
"[1] 0.9559559"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Calculate correlation coefficient\n",
"correlation_coefficient <- cor(ourdata$x, ourdata$y)\n",
"\n",
"# Print the correlation coefficient\n",
"correlation_coefficient"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "XLECQMwShRsC"
},
"source": [
"### 4.Fit a Linear Model"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 329
},
"id": "gTKg1fEghZ4E",
"outputId": "dbbe468f-30a4-4b6e-dcfc-93fa2a2a105b",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = y ~ x, data = ourdata)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-25.80 -17.60 -5.80 20.05 29.00 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) -47.00 16.42 -2.863 0.0211 * \n",
"x 228.00 24.75 9.212 1.56e-05 ***\n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 22.14 on 8 degrees of freedom\n",
"Multiple R-squared: 0.9139,\tAdjusted R-squared: 0.9031 \n",
"F-statistic: 84.86 on 1 and 8 DF, p-value: 1.561e-05\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Linear Regression Model\n",
"model <- lm(y~x, data = ourdata)\n",
"\n",
"#Model Summary\n",
"summary(model)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "8k1ogddQmBnO"
},
"source": [
"### 5.Get the Regression Equation"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "uFoXSzwsmJRt",
"outputId": "b7bb52cd-03ca-411a-fe4b-01e5bba762f7",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"y(hat) = 228 * x + ( -47 )"
]
}
],
"source": [
"#Define Coefficients\n",
"slope <- model$coefficients[2]\n",
"intercept <- model$coefficients[1]\n",
"\n",
"#Print the equation\n",
"cat( 'y(hat) = ', slope, '* x + (', intercept, ')')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "DMAjTUuQnk_z"
},
"source": [
"### 6.Make Predictions"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"id": "EHGPNUHxnqd9",
"outputId": "b3581283-1c49-4bcf-b2ac-35fbf371b83d",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"1: 67"
],
"text/latex": [
"\\textbf{1:} 67"
],
"text/markdown": [
"**1:** 67"
],
"text/plain": [
" 1 \n",
"67 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Predict y for x = 0.5\n",
"predict(model, newdata = data.frame(x=c(0.5)))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "rhzaqHlUoOHm"
},
"source": [
"## **Exercice 3**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "oY7xNsvPovi4"
},
"source": [
"### 1.Create a Data Frame\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 788
},
"id": "9SoZKgCGoSLe",
"outputId": "68d19774-beb4-45be-fca1-0eded8f27b52",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 22 × 2\n",
"\n",
"\t| direct_cost | month_nb |
|---|
\n",
"\t| <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| 10 | 3 |
\n",
"\t| 18 | 7 |
\n",
"\t| 24 | 10 |
\n",
"\t| 22 | 9 |
\n",
"\t| 27 | 11 |
\n",
"\t| 13 | 6 |
\n",
"\t| 10 | 5 |
\n",
"\t| 24 | 8 |
\n",
"\t| 25 | 7 |
\n",
"\t| 8 | 4 |
\n",
"\t| 16 | 6 |
\n",
"\t| 20 | 9 |
\n",
"\t| 28 | 12 |
\n",
"\t| 22 | 8 |
\n",
"\t| 19 | 10 |
\n",
"\t| 18 | 9 |
\n",
"\t| 26 | 11 |
\n",
"\t| 14 | 6 |
\n",
"\t| 20 | 8 |
\n",
"\t| 26 | 10 |
\n",
"\t| 30 | 12 |
\n",
"\t| 12 | 5 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 22 × 2\n",
"\\begin{tabular}{ll}\n",
" direct\\_cost & month\\_nb\\\\\n",
" & \\\\\n",
"\\hline\n",
"\t 10 & 3\\\\\n",
"\t 18 & 7\\\\\n",
"\t 24 & 10\\\\\n",
"\t 22 & 9\\\\\n",
"\t 27 & 11\\\\\n",
"\t 13 & 6\\\\\n",
"\t 10 & 5\\\\\n",
"\t 24 & 8\\\\\n",
"\t 25 & 7\\\\\n",
"\t 8 & 4\\\\\n",
"\t 16 & 6\\\\\n",
"\t 20 & 9\\\\\n",
"\t 28 & 12\\\\\n",
"\t 22 & 8\\\\\n",
"\t 19 & 10\\\\\n",
"\t 18 & 9\\\\\n",
"\t 26 & 11\\\\\n",
"\t 14 & 6\\\\\n",
"\t 20 & 8\\\\\n",
"\t 26 & 10\\\\\n",
"\t 30 & 12\\\\\n",
"\t 12 & 5\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 22 × 2\n",
"\n",
"| direct_cost <dbl> | month_nb <dbl> |\n",
"|---|---|\n",
"| 10 | 3 |\n",
"| 18 | 7 |\n",
"| 24 | 10 |\n",
"| 22 | 9 |\n",
"| 27 | 11 |\n",
"| 13 | 6 |\n",
"| 10 | 5 |\n",
"| 24 | 8 |\n",
"| 25 | 7 |\n",
"| 8 | 4 |\n",
"| 16 | 6 |\n",
"| 20 | 9 |\n",
"| 28 | 12 |\n",
"| 22 | 8 |\n",
"| 19 | 10 |\n",
"| 18 | 9 |\n",
"| 26 | 11 |\n",
"| 14 | 6 |\n",
"| 20 | 8 |\n",
"| 26 | 10 |\n",
"| 30 | 12 |\n",
"| 12 | 5 |\n",
"\n"
],
"text/plain": [
" direct_cost month_nb\n",
"1 10 3 \n",
"2 18 7 \n",
"3 24 10 \n",
"4 22 9 \n",
"5 27 11 \n",
"6 13 6 \n",
"7 10 5 \n",
"8 24 8 \n",
"9 25 7 \n",
"10 8 4 \n",
"11 16 6 \n",
"12 20 9 \n",
"13 28 12 \n",
"14 22 8 \n",
"15 19 10 \n",
"16 18 9 \n",
"17 26 11 \n",
"18 14 6 \n",
"19 20 8 \n",
"20 26 10 \n",
"21 30 12 \n",
"22 12 5 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ourdata <- data.frame(\n",
" direct_cost= c(10, 18, 24, 22, 27, 13, 10, 24, 25, 8, 16, 20, 28, 22, 19, 18, 26, 14, 20, 26, 30, 12 ),\n",
" month_nb= c(3, 7, 10, 9, 11, 6, 5, 8, 7, 4, 6, 9, 12, 8, 10, 9, 11, 6, 8, 10, 12, 5)\n",
")\n",
"\n",
"#Print the data\n",
"ourdata"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "NdCO7DuFsyX3"
},
"source": [
"**Which variable should we identify as dependent variable Y and which should we identify as explanatory variable X ?**\n",
"\n",
"---\n",
"\n",
"\n",
"\n",
"The dependent variable Y is (Direct Cost ) The explanatory variable X is (Month Number)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "TrfC4QwNs94c"
},
"source": [
"### 2.Plot the Data"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "pDShMswDtBcw",
"outputId": "6c62d03f-c239-4d03-8aac-4a534f9f270c",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
"Plot with title “Scatter Plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(ourdata$month_nb, ourdata$direct_cost, xlab = 'Month Number(I.V.)', ylab='Direct Cost(D.V.)', main = 'Scatter Plot')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "l7sYc_Dvt1S-"
},
"source": [
"**Does the scatterplot suggest a particular form of connection?**\n",
"\n",
"---\n",
"\n",
"\n",
"\n",
"Observing the plot, it’s evident that as x rises, Y also increases. Assuming a linear connection between x and y"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9UdVzFRZuKi7"
},
"source": [
"### 3.Regression Equation"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 173
},
"id": "RLrPJsz8uO3X",
"outputId": "0b7a5101-1843-492b-d2c3-c97ecf5b0bd7",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = direct_cost ~ month_nb, data = ourdata)\n",
"\n",
"Coefficients:\n",
"(Intercept) month_nb \n",
" 1.549 2.261 \n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" y(hat) = 2.26087 * x + ( 1.549407 )"
]
}
],
"source": [
"#Fit a Linear Model\n",
"model <- lm(direct_cost~month_nb, data = ourdata)\n",
"\n",
"#Model Summary\n",
"model\n",
"\n",
"#Define Coefficients\n",
"slope <- model$coefficients[2]\n",
"intercept <- model$coefficients[1]\n",
"\n",
"#Print the equation\n",
"cat( '\\n y(hat) = ', slope, '* x + (', intercept, ')')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "5HyeZNlev6NF"
},
"source": [
"### 4.Total Change in Direct Travel Cost (SST)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "TEZ8UEyXwD8b",
"outputId": "968dce54-c53b-4d37-85e0-3000204c27d3",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the total change in direct travel cost = 865.0909"
]
}
],
"source": [
"#Defining y\n",
"y <- ourdata$direct_cost\n",
"\n",
"#Finding the Mean\n",
"y_bar <- mean(y)\n",
"\n",
"#Finding SST\n",
"SST <- sum((y - y_bar)^ 2)\n",
"\n",
"#Print SST\n",
"cat('the total change in direct travel cost = ', SST)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "HlqPkxv4xTHO"
},
"source": [
"### 5.Explained Variation (SSR)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "-jRYz5ZbxZS0",
"outputId": "0d5f9a1d-80c6-4158-cfb2-cb1c464a3d9a",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the explained variation = 705.3913"
]
}
],
"source": [
"#Defining y_hat\n",
"y_hat <- model$fitted.values\n",
"\n",
"#Finding SSR\n",
"SSR <- sum((y_hat - y_bar)^ 2)\n",
"\n",
"#Print SSR\n",
"cat('the explained variation = ', SSR)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Y_kpZ1Yjx_Fg"
},
"source": [
"### 6.Residual Variation (SSE)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "fOhAERivxeXO",
"outputId": "a5fff807-19aa-4e4f-9f49-0a7179d63a66",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the residual variation = 159.6996"
]
}
],
"source": [
"#Finding SSE\n",
"SSE <- sum((y - y_hat)^ 2)\n",
"\n",
"#Print SSE\n",
"cat('the residual variation = ', SSE)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "YfEJANRtypUK"
},
"source": [
"### 7.Coefficient of Determination (R squared)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "Xl9tqePY1T3Z",
"outputId": "83ce8283-28d8-46e4-e289-7e4415aa4036",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the coefficient of determination = 0.8153956"
]
}
],
"source": [
"#Finding R squared\n",
"R_squared <- SSR/SST\n",
"\n",
"#Print R squared\n",
"cat('the coefficient of determination = ', R_squared)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "7hd0U0B518zF"
},
"source": [
"Interpretation:\n",
"\n",
"---\n",
"\n",
"\n",
"the coefficient of determination(0.8153956)\n",
"is close to 1. This suggests that approximately 81.54% of the variability in the 'Direct Cost' (dependent variable) can be explained by the linear regression model with the Number of Month ( independent variable)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "zl6gaGTP3ROX"
},
"source": [
"# **TD2**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Ygog8ivQ3V-t"
},
"source": [
"## **Exercice 2**\n",
"In the Europe.xlsx file, you will find the population and area of 27 European countries.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "2juR5NJV5-el"
},
"source": [
"### 1.Load Data"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 175
},
"id": "Rn9ngggK6ICq",
"outputId": "4019209d-35c2-4730-ad71-d91af8a25358",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"ename": "ERROR",
"evalue": "Error: `path` does not exist: ‘Europe.xlsx’\n",
"output_type": "error",
"traceback": [
"Error: `path` does not exist: ‘Europe.xlsx’\nTraceback:\n",
"1. read_excel(\"Europe.xlsx\")",
"2. check_file(path)",
"3. stop(\"`path` does not exist: \", sQuote(path), call. = FALSE)"
]
}
],
"source": [
"#Import the readxl library\n",
"library(readxl)\n",
"\n",
"#Read the Data File\n",
"Europe <- read_excel('Europe.xlsx')\n",
"\n",
"#Display Data\n",
"Europe"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "2pqghDZs7y2t",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"#Rename Columns\n",
"colnames(Europe)[3] = \"population\"\n",
"colnames(Europe)[4] = \"area\"\n",
"\n",
"#Display\n",
"Europe"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "xOuyAM5x9yYx"
},
"source": [
"### 2.Linear Adjustment"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "H884XKAN-J2M"
},
"source": [
"***Does a linear adjustment seem justified? What coefficient should you calculate with R?***\n",
"\n",
"---\n",
"\n",
"\n",
"\n",
"To determine if a linear adjustment is justified, you can create a scatter plot of the data and visually inspect whether the points roughly form a straight line."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "2Fkwppkz-Tll",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"#Draw the scatter Plot\n",
"plot(Europe$area, Europe$population, xlab='Area(x)', ylab='Population(y)', main='Scatter Plot')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tGIAmhQb_KYK"
},
"source": [
"From the following scatter plot we notice that in general, as the Area increase the Population increases.This trend probably indicates a potential linear relationship between the area and the population"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "bDZKf5nG_zN2"
},
"source": [
"Additionaly we can calculate the correlation coefficient(r) to quantify the strenght and direction of the linear relationship between the two variables"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "3-l0K2H7_uH3",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"#Find the correlation coefficient\n",
"r <- cor(Europe$area, Europe$population)\n",
"\n",
"#Print r\n",
"r"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "RSNphsuhAyIT"
},
"source": [
"We get the correlation coefficient(r = 0.71521111634042), wich is close to 1. That suggests a positive strong relationship between the area and the population"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "KTZw_El2BZCJ"
},
"source": [
"### 3.Regression Equation"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "Zg1F-YzYBi6D",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"#Fit a Linear Model\n",
"model <- lm(population~area, data = Europe)\n",
"\n",
"#Model Summary\n",
"model\n",
"\n",
"#Define Coefficients\n",
"slope <- model$coefficients[2]\n",
"intercept <- model$coefficients[1]\n",
"\n",
"#Print the equation\n",
"cat( '\\n y(hat) = ', slope, '* x + (', intercept, ')')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "KfDEXByGEVcT"
},
"source": [
"### 4.Residuals"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "xEHtZbYQEX2u",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"#Calculate the residuals\n",
"residuals <- model$residuals\n",
"\n",
"#Print residuals\n",
"residuals\n",
"\n",
"#Residuals mean = 0?\n",
"residuals_mean <- mean(residuals)\n",
"residuals_mean\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "wtvheUgnFntG"
},
"source": [
"### 5.Error Variance Estimator (s squared)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "A_avTZKxF8Yu",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"#Define y\n",
"y <- Europe$population\n",
"\n",
"#Define y_hat(predicted values)\n",
"y_hat <- model$fitted.values\n",
"\n",
"#Calculate SSE\n",
"SSE <- sum((y - y_hat)^ 2)\n",
"\n",
"#Calculate s squared\n",
"s_squared <- SSE / length(y) - 2\n",
"\n",
"#Print s squared\n",
"cat(' The Error Variance Estimator = ', s_squared)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "6rmYdxFLIODO"
},
"source": [
"### 6.The Variance Estimators of 𝛽0 and 𝛽1 (S𝛽0 &S𝛽1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "45CbT286IaVL",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"#Define x\n",
"x <- Europe$area\n",
"\n",
"#Find the mean of x\n",
"x_bar <- mean(x)\n",
"\n",
"#Calculate the Variance Estimators of 𝛽0\n",
"SB0 <- s_squared * ( sum(x^2) / ( length(y) * sum((x - x_bar )^2)) )\n",
"\n",
"#Print S𝛽0\n",
"cat('The Variance Estimators of 𝛽0 = ', SB0)\n",
"\n",
"#Calculate the Variance Estimators of 𝛽1\n",
"SB1 <- s_squared / ( sum((x - x_bar )^2) )\n",
"\n",
"#Print S𝛽0\n",
"cat('\\n The Variance Estimators of 𝛽1 = ', SB1)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "bEQmv2SMKssQ"
},
"source": [
"### 7.Confidence Interval for the parameter 𝛽0"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 156
},
"id": "D9FvnPuyK9Ke",
"outputId": "b0408464-a8e0-422a-fc33-69cfdcd7fdb5",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the Confidence Interval for the parameter 𝛽0 : 3018.959 3670.02"
]
},
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = y ~ x, data = ourdata)\n",
"\n",
"Coefficients:\n",
"(Intercept) x \n",
" 3344.49 -17.01 \n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Find the Interval\n",
"B0_CI <- confint(object = model, parm=\"(Intercept)\", level = .95)\n",
"\n",
"#Print the Interval\n",
"cat('the Confidence Interval for the parameter 𝛽0 : ', B0_CI)\n",
" model\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "o3xLObifNuvV"
},
"source": [
"### 8.Confidence Interval for the parameter 𝛽1"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "BZ1Mo7ZqNyrn",
"outputId": "e4f79620-3df9-4cb9-c7dd-a16fe8f17200",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the Confidence Interval for the parameter 𝛽1 : -25.40835 -8.615725"
]
}
],
"source": [
"#Find the Interval\n",
"B1_CI <- confint(object = model, parm=\"x\", level = .95)\n",
"\n",
"#Print the Interval\n",
"cat('the Confidence Interval for the parameter 𝛽1 : ', B1_CI)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "yF6vSIp9OKwl"
},
"source": [
"### 9.Hypothesis Testing for 𝛽0"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "cK1zsEI7Ok2B"
},
"source": [
"**Step1: Set the Hypothesis**\n",
"\n",
"---\n",
"H0: 𝛽0 = 0\n",
"\n",
"H1: 𝛽0 ≠ 0\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4k8nP8coRsLQ"
},
"source": [
"**Step2: Test-Statistic**\n",
"\n",
"---\n",
"T-test for significance\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "7XHm9X8aR3kQ",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"# find t-value\n",
"t <- model$coefficients[1] / SB0\n",
"\n",
"cat(\"t - value = \", t)\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "2WAKO_SzT9X5"
},
"source": [
"**Step3: T-Critical**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "pi7xJcUzUhUq",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"# find t-critical\n",
"t_critical <- qt(df= length(y) -2, p=0.025)\n",
"\n",
"cat( \"t-critical: \",abs(t_critical))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "5G1NtFcIXEif"
},
"source": [
"### 10.Anova"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 140
},
"id": "hH8-nVboXMlK",
"outputId": "124e6a15-7b08-4cb6-a490-3a8c25a783ae",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"ename": "ERROR",
"evalue": "Error in eval(expr, envir, enclos): object 'Europe' not found\n",
"output_type": "error",
"traceback": [
"Error in eval(expr, envir, enclos): object 'Europe' not found\nTraceback:\n",
"1. anova(Europe)"
]
}
],
"source": [
"anova(Europe)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "SpupjfD-TXq2"
},
"source": [
"## **Exercice 4**\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "D1cg3W09UAYc"
},
"source": [
"### 1.Create a Data Frame\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "LxWT3vTNUAY7",
"vscode": {
"languageId": "r"
}
},
"outputs": [],
"source": [
"ourdata <- data.frame(\n",
" x= c(4 , 5.7 , 4.9 , 3 , 14.8 , 69.6 , 63.8 , 26.2 , 38.3 , 24.7 , 67.5 ),\n",
" y= c(3432 , 3273 , 3049 , 3642 , 3394 , 2628 , 2204 , 2643 , 2192 , 2687 , 2159 )\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "raJH-BDLUAY9"
},
"source": [
"### 2.Display the Data"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 460
},
"id": "-HxvLnPEUAY-",
"outputId": "2a128c5c-3043-4837-e612-514b4ab89195",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 11 × 2\n",
"\n",
"\t| x | y |
|---|
\n",
"\t| <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| 4.0 | 3432 |
\n",
"\t| 5.7 | 3273 |
\n",
"\t| 4.9 | 3049 |
\n",
"\t| 3.0 | 3642 |
\n",
"\t| 14.8 | 3394 |
\n",
"\t| 69.6 | 2628 |
\n",
"\t| 63.8 | 2204 |
\n",
"\t| 26.2 | 2643 |
\n",
"\t| 38.3 | 2192 |
\n",
"\t| 24.7 | 2687 |
\n",
"\t| 67.5 | 2159 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 11 × 2\n",
"\\begin{tabular}{ll}\n",
" x & y\\\\\n",
" & \\\\\n",
"\\hline\n",
"\t 4.0 & 3432\\\\\n",
"\t 5.7 & 3273\\\\\n",
"\t 4.9 & 3049\\\\\n",
"\t 3.0 & 3642\\\\\n",
"\t 14.8 & 3394\\\\\n",
"\t 69.6 & 2628\\\\\n",
"\t 63.8 & 2204\\\\\n",
"\t 26.2 & 2643\\\\\n",
"\t 38.3 & 2192\\\\\n",
"\t 24.7 & 2687\\\\\n",
"\t 67.5 & 2159\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 11 × 2\n",
"\n",
"| x <dbl> | y <dbl> |\n",
"|---|---|\n",
"| 4.0 | 3432 |\n",
"| 5.7 | 3273 |\n",
"| 4.9 | 3049 |\n",
"| 3.0 | 3642 |\n",
"| 14.8 | 3394 |\n",
"| 69.6 | 2628 |\n",
"| 63.8 | 2204 |\n",
"| 26.2 | 2643 |\n",
"| 38.3 | 2192 |\n",
"| 24.7 | 2687 |\n",
"| 67.5 | 2159 |\n",
"\n"
],
"text/plain": [
" x y \n",
"1 4.0 3432\n",
"2 5.7 3273\n",
"3 4.9 3049\n",
"4 3.0 3642\n",
"5 14.8 3394\n",
"6 69.6 2628\n",
"7 63.8 2204\n",
"8 26.2 2643\n",
"9 38.3 2192\n",
"10 24.7 2687\n",
"11 67.5 2159"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ourdata"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "mIRluHpCW6KY"
},
"source": [
"### 3.Plot the Data"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "jsRK8YMIW6KZ",
"outputId": "0d83c6cf-d9d9-4d51-8cba-27534e93ce69",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Plot with title “Scatter Plot”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(ourdata$x, ourdata$y, xlab='Independent Variable(x)', ylab = 'Dependent Variable(y)', main = 'Scatter Plot')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LVaqmbEbXQ19"
},
"source": [
"### 4.Fit a Linear Model"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 329
},
"id": "xeyqvQ9gXQ1_",
"outputId": "7a2c2cec-3079-4b9a-b48e-df85405b6dca",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = y ~ x, data = ourdata)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-500.93 -224.71 -37.18 228.42 467.55 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 3344.489 143.903 23.241 2.41e-09 ***\n",
"x -17.012 3.712 -4.583 0.00132 ** \n",
"---\n",
"Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
"\n",
"Residual standard error: 312.3 on 9 degrees of freedom\n",
"Multiple R-squared: 0.7001,\tAdjusted R-squared: 0.6668 \n",
"F-statistic: 21.01 on 1 and 9 DF, p-value: 0.001321\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"model <- lm(y~x, data = ourdata)\n",
"summary(model)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4r1tFF27XQ2A"
},
"source": [
"### 5.Get the Coefficients (Slope & Intercept)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "PYPh4xDMXQ2B",
"outputId": "74ef8cef-3dc6-4784-ea46-a1653e186c5e",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Slope: -17.01204 \n",
"Intercept: 3344.489"
]
}
],
"source": [
"slope <- model$coefficients[2]\n",
"Intercept <- model$coefficients[1]\n",
"cat('Slope: ', slope, '\\n')\n",
"cat('Intercept: ',Intercept )"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "xomb6q-rXmac"
},
"source": [
"### 6.Visualization of the regression line"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "mFZKEyavXmad",
"outputId": "b9d1b268-5e44-448e-f513-64f50e3ae3fb",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Plot with title “Linear Regression Model”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"#Scatter Plot with The 'best-fit line'\n",
"plot(ourdata$x, ourdata$y, xlab='Independent Variable(x)', ylab = 'Dependent Variable(y)', main = 'Linear Regression Model', col='blue')\n",
"abline(a=Intercept, b=slope, col='red')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Xw8FSb9QX0Yd"
},
"source": [
"### 7.Confidence Interval for the parameter 𝛽1"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "joFwmwGzX0Ye",
"outputId": "18f3364a-08e1-468c-e3f1-40fb6318be57",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the Confidence Interval for the parameter 𝛽1 : -25.40835 -8.615725"
]
}
],
"source": [
"#Find the Interval\n",
"B1_CI <- confint(object = model, parm=\"x\", level = .95)\n",
"\n",
"#Print the Interval\n",
"cat('the Confidence Interval for the parameter 𝛽1 : ', B1_CI)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4Otga5NjaH7u"
},
"source": [
"### 8.Anova"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 161
},
"id": "RbU2B7tZaH7w",
"outputId": "dd10198d-91de-4ec2-e6e1-44c5c3110a43",
"vscode": {
"languageId": "r"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A anova: 2 × 5\n",
"\n",
"\t | Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|
\n",
"\t | <int> | <dbl> | <dbl> | <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| x | 1 | 2048930.3 | 2048930.32 | 21.00783 | 0.001321341 |
|---|
\n",
"\t| Residuals | 9 | 877785.9 | 97531.76 | NA | NA |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A anova: 2 × 5\n",
"\\begin{tabular}{r|lllll}\n",
" & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
" & & & & & \\\\\n",
"\\hline\n",
"\tx & 1 & 2048930.3 & 2048930.32 & 21.00783 & 0.001321341\\\\\n",
"\tResiduals & 9 & 877785.9 & 97531.76 & NA & NA\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A anova: 2 × 5\n",
"\n",
"| | Df <int> | Sum Sq <dbl> | Mean Sq <dbl> | F value <dbl> | Pr(>F) <dbl> |\n",
"|---|---|---|---|---|---|\n",
"| x | 1 | 2048930.3 | 2048930.32 | 21.00783 | 0.001321341 |\n",
"| Residuals | 9 | 877785.9 | 97531.76 | NA | NA |\n",
"\n"
],
"text/plain": [
" Df Sum Sq Mean Sq F value Pr(>F) \n",
"x 1 2048930.3 2048930.32 21.00783 0.001321341\n",
"Residuals 9 877785.9 97531.76 NA NA"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"anova(model)"
]
}
],
"metadata": {
"colab": {
"provenance": [],
"toc_visible": true
},
"kernelspec": {
"display_name": "R",
"name": "ir"
},
"language_info": {
"name": "R"
}
},
"nbformat": 4,
"nbformat_minor": 0
}