Name Final Midterm1 Midterm2 Project Homework Timothy F. 117 82 30 10.5 61 Karen
ID: 3323107 • Letter: N
Question
Name Final Midterm1 Midterm2 Project Homework Timothy F. 117 82 30 10.5 61 Karen E. 183 96 68 11.3 72 Verena 124 57 82 11.3 69 Elizabeth L. 169 88 86 10.6 84 Patrick M. 164 93 81 10 71 Julia E. 134 90 83 11.3 79 Thomas A. 98 83 21 11.2 51 Marshall K. 136 59 62 9.1 58 Justin E. 183 89 57 10.7 79 Alexandra E. 171 83 86 11.5 78 Christopher B. 173 95 75 8 77 Justin C. 164 81 66 10.7 66 Miguel A. 150 86 63 8 74 Brian J. 153 81 86 9.2 76 Gregory J. 149 81 87 9.2 75 Kristina G. 178 98 96 9.3 84 Timothy B. 75 50 27 10 20 Jason C. 159 91 83 10.6 71 Whitney E. 157 87 89 10.5 85 Alexis P. 158 90 91 11.3 68 Nicholas T. 171 95 82 10.5 68 Amandeep S. 173 91 37 10.6 54 Irena R. 165 93 81 9.3 82 Yvon T. 168 88 66 10.5 82 Sara M. 186 99 90 7.5 77 Annie P. 157 89 92 10.3 68 Benjamin S. 177 87 62 10 72 David W. 170 92 66 11.5 78 Josef H. 78 62 43 9.1 56 Rebecca S. 191 93 87 11.2 80 Joshua D. 169 95 93 9.1 87 Ian M. 170 93 65 9.5 66 Katharine A. 172 92 98 10 77 Emily R. 168 91 95 10.7 83 Brian M. 179 92 80 11.5 82 Shad M. 148 61 58 10.5 65 Michael R. 103 55 65 10.3 51 Israel 144 76 88 9.2 67 Iris J. 155 63 62 7.5 67 Mark G. 141 89 66 8 72 Peter H. 138 91 42 11.5 66 Catherine R.M. 180 90 85 11.2 78 Christina M. 120 75 62 9.1 72 Enrique J. 86 75 46 10.3 72 Sarah K. 151 91 65 9.3 77 Thomas J. 149 84 70 8 70 Sonya 163 94 92 10.5 81 Michael B. 153 93 78 10.3 72 Wesley M. 172 91 58 10.5 66 Mark R. 165 91 61 10.5 79 Adam J. 155 89 86 9.1 62 Jared A. 181 98 92 11.2 83 Michael T. 172 96 51 9.1 83 Kathryn D. 177 95 95 10 87 Nicole M. 189 98 89 7.5 77 Wayne E. 161 89 79 9.5 44 Elizabeth S. 146 93 89 10.7 73 John R. 147 74 64 9.1 72 Valentin 160 97 96 9.1 80 David T. O. 159 94 90 10.6 88 Marc I. 101 81 89 9.5 62 Samuel E. 154 94 85 10.5 76 Brooke S. 183 92 90 9.5 86 1. Use backwards elimination to create the "best" model for predicting "Final" starting with Midterm1, Midterm2, Project, and Homework. Write the final regression equation, the R-squared/Adjusted R-squared and include the final output from your regression. Write a brief summary of your analysis that would be suitable for an email to your boss. Grades.xlsExplanation / Answer
The full model involving all variables returned with Multiple R-squared: 0.5899, Adjusted R-squared: 0.5616
the variables that are significant are Midterm1 and Homework
the other two variables Midterm2 and Project did not turn out to be significant.
The step wise backward elimiation return model with Midterm1, Midterm2 and Homework.
The equation is as thus
Final = 0.6469 + 1.1640 * Midterm1 + 0.2479 * Midterm2 + 0.4933 * Homework
Multiple R-squared: 0.5897, Adjusted R-squared: 0.5689
The Midterm1, Midterm2 and Homework have positive impact on scoring good grade in Final.
The Final Grade is mostly impacted 1.16 times scored in Midterm1
then impacted by HomeWork i.e, every additional unit in homework increases Final Grade by 0.4933
The Final Grade is lastly impacted 0.2479 times scored in Midterm2
56% of the variation is explained by the variables in the model.
The inference is that who do well early(Midterm1) and who are disciplined in Homework get good grades in Final
*******************************R Code for the problem*******************************
>grades=read.csv("D:\grades.csv", row.names = 1, header= TRUE)
>fullmodel <- lm(Final ~ Midterm1 + Midterm2 + Project + Homework, data = grades)
>summary(fullmodel)
*******************************R-Output Starts*******************************
lm(formula = Final ~ Midterm1 + Midterm2 + Project + Homework, data = grades)
Residuals:
Min 1Q Median 3Q Max
-48.796 -9.205 -0.342 10.905 31.921
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.3998 26.2770 0.129 0.8975
Midterm1 1.1665 0.2492 4.680 1.76e-05 ***
Midterm2 0.2461 0.1526 1.612 0.1123
Project -0.2910 2.0806 -0.140 0.8893
Homework 0.4943 0.2770 1.784 0.0796 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 17.68 on 58 degrees of freedom
Multiple R-squared: 0.5899, Adjusted R-squared: 0.5616
F-statistic: 20.86 on 4 and 58 DF, p-value: 1.077e-10
*******************************R-Output Ends*******************************
>step(fullmodel, direction = "backward", trace=TRUE )
*******************************R-Output Starts*******************************
Start: AIC=366.69
Final ~ Midterm1 + Midterm2 + Project + Homework
Df Sum of Sq RSS AIC
- Project 1 6.1 18128 364.71
<none> 18122 366.69
- Midterm2 1 812.2 18934 367.45
- Homework 1 994.7 19117 368.06
- Midterm1 1 6844.7 24967 384.88
Step: AIC=364.71
Final ~ Midterm1 + Midterm2 + Homework
Df Sum of Sq RSS AIC
<none> 18128 364.71
- Midterm2 1 831.1 18959 365.54
- Homework 1 991.4 19119 366.07
- Midterm1 1 6850.4 24978 382.91
Call:
lm(formula = Final ~ Midterm1 + Midterm2 + Homework, data = grades)
Coefficients:
(Intercept) Midterm1 Midterm2 Homework
0.6469 1.1640 0.2479 0.4933
*******************************R-Output Ends*******************************
>reducedmodel1 <- lm(Final ~ Midterm1 + Midterm2 + Homework, data = grades)
>summary(reducedmodel1)
*******************************R-Output Starts*******************************
Call:
lm(formula = Final ~ Midterm1 + Midterm2 + Homework, data = grades)
Residuals:
Min 1Q Median 3Q Max
-48.869 -9.291 -0.406 10.754 32.598
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.6469 17.2618 0.037 0.9702
Midterm1 1.1640 0.2465 4.722 1.48e-05 ***
Midterm2 0.2479 0.1507 1.645 0.1054
Homework 0.4933 0.2746 1.796 0.0776 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 17.53 on 59 degrees of freedom
Multiple R-squared: 0.5897, Adjusted R-squared: 0.5689
F-statistic: 28.27 on 3 and 59 DF, p-value: 1.855e-11
*******************************R-Output Ends*******************************
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