Use backwards elimination to create the “best” model for predicting “Final” star

Question

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.

Name Final Midterm1 Homework Project Midterm2 Timothy F. 117 82 61 10.5 30 Karen E. 183 96 72 11.3 68 Verena 124 57 69 11.3 82 Elizabeth L. 169 88 84 10.6 86 Patrick M. 164 93 71 10 81 Julia E. 134 90 79 11.3 83 Thomas A. 98 83 51 11.2 21 Marshall K. 136 59 58 9.1 62 Justin E. 183 89 79 10.7 57 Alexandra E. 171 83 78 11.5 86 Christopher B. 173 95 77 8 75 Justin C. 164 81 66 10.7 66 Miguel A. 150 86 74 8 63 Brian J. 153 81 76 9.2 86 Gregory J. 149 81 75 9.2 87 Kristina G. 178 98 84 9.3 96 Timothy B. 75 50 20 10 27 Jason C. 159 91 71 10.6 83 Whitney E. 157 87 85 10.5 89 Alexis P. 158 90 68 11.3 91 Nicholas T. 171 95 68 10.5 82 Amandeep S. 173 91 54 10.6 37 Irena R. 165 93 82 9.3 81 Yvon T. 168 88 82 10.5 66 Sara M. 186 99 77 7.5 90 Annie P. 157 89 68 10.3 92 Benjamin S. 177 87 72 10 62 David W. 170 92 78 11.5 66 Josef H. 78 62 56 9.1 43 Rebecca S. 191 93 80 11.2 87 Joshua D. 169 95 87 9.1 93 Ian M. 170 93 66 9.5 65 Katharine A. 172 92 77 10 98 Emily R. 168 91 83 10.7 95 Brian M. 179 92 82 11.5 80 Shad M. 148 61 65 10.5 58 Michael R. 103 55 51 10.3 65 Israel 144 76 67 9.2 88 Iris J. 155 63 67 7.5 62 Mark G. 141 89 72 8 66 Peter H. 138 91 66 11.5 42 Catherine R.M. 180 90 78 11.2 85 Christina M. 120 75 72 9.1 62 Enrique J. 86 75 72 10.3 46 Sarah K. 151 91 77 9.3 65 Thomas J. 149 84 70 8 70 Sonya 163 94 81 10.5 92 Michael B. 153 93 72 10.3 78 Wesley M. 172 91 66 10.5 58 Mark R. 165 91 79 10.5 61 Adam J. 155 89 62 9.1 86 Jared A. 181 98 83 11.2 92 Michael T. 172 96 83 9.1 51 Kathryn D. 177 95 87 10 95 Nicole M. 189 98 77 7.5 89 Wayne E. 161 89 44 9.5 79 Elizabeth S. 146 93 73 10.7 89 John R. 147 74 72 9.1 64 Valentin 160 97 80 9.1 96 David T. O. 159 94 88 10.6 90 Marc I. 101 81 62 9.5 89 Samuel E. 154 94 76 10.5 85 Brooke S. 183 92 86 9.5 90

Explanation / Answer

We use Minitab to answer-

Regression Analysis: Final versus Midterm1, Midterm2, Project, Homework

Backward Elimination of Terms

to remove = 0.1

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 25227 12613.7 39.92 0.000
Midterm1 1 7514 7514.2 23.78 0.000
Homework 1 2557 2557.0 8.09 0.006
Error 60 18959 316.0
Total 62 44187

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -0.2 17.5 -0.01 0.993
Midterm1 1.211 0.248 4.88 0.000 1.63
Homework 0.702 0.247 2.84 0.006 1.63

Regression Equation

Final = -0.2 + 1.211 Midterm1 + 0.702 Homework

Fits and Diagnostics for Unusual Observations

Obs Final Fit Resid Std Resid
3 124.00 117.33 6.67 0.41 X
7 98.00 136.17 -38.17 -2.25 R
17 75.00 74.44 0.56 0.04 X
29 78.00 114.26 -36.26 -2.13 R
44 86.00 141.24 -55.24 -3.17 R
56 161.00 138.52 22.48 1.40 X
61 101.00 141.48 -40.48 -2.31 R

R Large residual
X Unusual X

The variable Project And Midterm 2 can be elliminated by Backward ellimination process.

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