A guidance counselor wanted to
A guidance counselor wanted to see if she could predictedstudent’s GPAs in college. She decided to she collected the HighSchool GPA, SAT Score, and if the student was involved in anextracurricular activity in High School of eight students and foundout their GPA in their first year of college.
| HS GPA | SAT | EXTRA | COLLEGE GPA |
| 3.5 | 1230 | no | 3.4 |
| 2.8 | 1070 | yes | 3.0 |
| 2.5 | 1090 | no | 2.7 |
| 3.7 | 1280 | no | 3.6 |
| 3.2 | 1130 | yes | 3.5 |
| 3.1 | 1300 | yes | 3.3 |
| 3.9 | 1290 | no | 3.6 |
| 2.6 | 1020 | yes | 2.9 |
a.) Provide an equation that can be used to predict College GPAbased on the 3 independent variables given above.
b.) Explain what the coefficient of the “Extra” variablemeans.
c.) What is the p-value of the overall model? Is the overallmodel significant at the ? = 0.05 level?
d.) List out and explain what the p-values for the individualvariables mean.
e.) Were there any variables shown in part d that were notsignificant? If so remove them and give a new regression model. Isit better than in part a? Worse? Why? If it is better use this newone for the remaining problems. Use overall p-value, R2, individualvariable p-values, etc to support your case.
f.) Suppose we wanted to make a prediction for the College GPAfor a student who had a 3.2 high school GPA, scored a 1280 on herSATs, and participated in band. Use whichever model you decided wasthe best in part e. Also give a 95% prediction interval for yourprediction for College GPA from the Excel output of whichever modelyou chose.
Answer:
a) Regression Analysis: COLLEGE GPA versus HS GPA, SAT,EXTRA_yes
The regression equation isCOLLEGE GPA = 0.805 + 0.719 HS GPA + 0.000062 SAT + 0.197EXTRA_yes
b) If the student was involed in an extra curricular activity inshcools then Extra variable is YES i.e. 1 or not involed in anextracurricular activity then it is NO i.e. 0
c)P-value of regresssion is 0.004 < alpha 0.05. so we concludethat the regression equation is best fit to the given data
d)P-value of HS GPA = 0.005P-value of SAT = 0.919P-value Extra_yes = 0.064
e) Here Onle one independent variable of HS_GPA issignificantsince its p-value < alpha 0.05.The remaining two variables SAT and Extra_Yes are no significantsince Its p-value > alpha 0.05.R-square = 0.956 and Standard error of residuals = 0.094925
From the MINITAB Output,
Now we eliminate SAT and Extra_yes variables. The new regressionequation is
P-value of regression is 0.001< alpha 0.05. so we concludethat the regression equation is best fit to the given data
but R-square = 0.885 and S = 0.125495 which is higher thanprevious model.Thus previous model is best model compare to this model.
g)
The regression equation isCOLLEGE GPA = 0.805 + 0.719 (3.2) + 0.000062 (1280) + 0.197(1) =3.3820
e) e) The 95% prediction interval for your prediction forCollege GPA is (3.0399, 3.7241)
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