Question

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	2.13	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

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?

Answer 1

using excel>data >data analysis >Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.906854
R Square	0.822383
Adjusted R Square	0.78686
Standard Error	0.501071
Observations	19
ANOVA
	df	SS	MS	F	Significance F
Regression	3	17.43737	5.812455	23.15051	7E-06
Residual	15	3.766087	0.251072
Total	18	21.20345
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-2.96382	0.683133	-4.33856	0.000585	-4.41988	-1.50775
HSGPA	0.024894	0.20413	0.121952	0.904556	-0.4102	0.459986
SAT	0.003718	0.00074	5.027318	0.00015	0.002142	0.005294
REF	0.19632	0.108629	1.807251	0.090819	-0.03522	0.427857

a ) the model is

CGPA = -2.964 + 0.0249*HSGPA +0.00372*SAT +0.19632*REF

b ) since p value of f stat is 0.000 which is less than 0.05 so we conclude that model is significant to use

c) variable HSGPA and REF is not good predictor because their p value is greater than 0.05