Question

Statistics concepts for engineering management:

The data in the table provides: College GPA, High School GPA, SAT total score, and number of letters of reference.
   a. Generate a model for college GPA as a function of the other three variables.
   b. Is this model useful? Justify your conclusion.
   c. Are any of the variables not useful predictors? Why?

CGPA   HSGPA   SAT   REF
2.04 2.01   1070   5
2.56 3.4   1254   6
3.75 3.68   1466   6
1.1 1.54   706   4
3 3.32   1160   5
0.05 0.33   756   3
1.38 0.36   1058   2
1.5 1.97   1008   7
1.38 2.03   1104   4
4.01 2.05   1200   7
1.5 2.1 896   7
1.29 1.34 848   3
1.9 1.51 958   5
3.11 3.12 1246   6
1.92 2.14 1106   4
0.81 2.6 790   5
1.01 1.9 954   4
3.66 3.06 1500   6
2 1.6    1046   5

Answer 1

a.)

Below output was generated using regression from excel data analysis addin.

Model was built using CGPA as the dependent variable Vs HSGPA,SAT, REF as dependent variables.

Model coefficients are highlighted in green below. Model performance measures highlighted in yellow.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.906865294
R Square	0.822404661
Adjusted R Square	0.786885593
Standard Error	0.501041207
Observations	19
ANOVA
	df	SS	MS	F	Significance F
Regression	3	17.43781827	5.812606091	23.15389203	6.99009E-06
Residual	15	3.765634359	0.251042291
Total	18	21.20345263
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-2.961593238	0.683200733	-4.334880066	0.000589025	-4.417801129	-1.505385346
HSGPA	0.026328666	0.203880871	0.1291375	0.898964517	-0.408233124	0.460890456
SAT	0.003714768	0.000740799	5.014542902	0.000153971	0.002135793	0.005293744
REF	0.195979969	0.108310436	1.809428306	0.090465946	-0.034878261	0.4268382

b.)

Yes model is useful since it performs well.

1. Adjusted R Square value of 0.787 seems reasonable.

2. Also the f-test is found to reject H0: regression model does not explain the variance at significance level .05. Highlighted in blue.

c.)

HSGPA is not useful for the model as suggested by the t-test result which shows p-value of 0.8989 which implies fail to reject H0: coefficient = 0 at .05 level of significance.

This is also supported by the plot of CGPA against HSGPA which shows little linear relationship between the variables.

	Coefficients	Standard Error	t Stat	P-value
Intercept	-2.961593238	0.683200733	-4.334880066	0.000589025
HSGPA	0.026328666	0.203880871	0.1291375	0.898964517
SAT	0.003714768	0.000740799	5.014542902	0.000153971
REF	0.195979969	0.108310436	1.809428306	0.090465946