Question

QUESTION 3

1. The following table contains ACT scores and the GPA for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal.

   Student	GPA	ACT
   1	2.8	21
   2	3.4	24
   3	3	26
   4	3.5	27
   5	3.6	29
   6	3	25
   7	2.7	25
   8	3.7	30

   You estimate the following relationship between GPA and ACT:

   SUMMARY OUTPUT
   Regression Statistics
   Multiple R	0.759884064
   R Square	0.577423791
   Adjusted R Square	0.506994423
   Standard Error	0.269173202
   Observations	8
   ANOVA
   	df	SS	MS	F	Significance F
   Regression	1	0.594024725	0.594024725	8.198622346	0.0286766
   Residual	6	0.434725275	0.072454212
   Total	7	1.02875
   	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
   Intercept	0.568131868	0.928421385	0.611933199	0.563036476	-1.703633417	2.839897154
   ACT	0.102197802	0.035692019	2.863323654	0.0286766	0.014862578	0.189533026

   a). (5) Compute the value of the least squares residual for the first student in the sample. Show your calculation.

   b). (5) Interpret the intercept.

   c). (5) Interpret the slope.

   d). (10) Using the critical value approach, test whether we have a positive significant relationship between ACT and GPA. Set up the null and alternative. Use a level of significance of 5%.

Answer 1