Question

1.Interpret the following results of multiple regression. Interpret each statistic (b and beta) for each independent variable and the intercept. Provide a complete interpretation using the five-step model of hypothesis testing.

Regression: The Relationship Between Number of Math Courses Taken, High School Grade Point Average, College Grade Point Average and Score on Stat Final

               Variables Entered/Removed(b)

Model	Variables Entered	Variables Removed	Method
1	Number of Math Courses taken, High School Grade Point Average, College Grade Point Average(a)	.	Enter

a All requested variables entered.

b Dependent Variable: Score on Stat Final

                                   Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.898(a)	.806	.797	6.117

a Predictors: (Constant), Number of Math Courses taken, High School Grade Point Average, College Grade Point Average

                                                           ANOVA(b)

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	9961.322	3	3320.441	88.733	.000(a)
	Residual	2394.914	64	37.421
	Total	12356.235	67

a Predictors: (Constant), Number of Math Courses taken, High School Grade Point Average, College Grade Point Average

b Dependent Variable: Score on Stat Final

                                                              Coefficients(a)

  

  

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1
	(Constant)	-8.251	2.882		-2.863	.006
	High School Grade Point Average	5.095	1.195	.271	4.263	.000
	College Grade Point Average	9.915	1.161	.581	8.540	.000
Number of Math Courses taken	2.901	.679	.261	4.271	.000

a Dependent Variable: Score on Stat Final

Answer 1

Hypotehsis testing:

H0:slope=0

H1:atleast one of the slope not =0

alpha=0.05

F=88.733

p=.000

Model is significant

Reject Null hypothesis.

There is suffiicient statistical evidence at 5% level of significance to conclude that the slopes of regression line are not equal to zero.

For (Constant) t=-2.83 p=0.06

p>0.05

Y intercept is not signficant.

For Number of Math Courses taken t=4.271,p=0.000

p<0.05

Number of Math Courses is significant variable.

For High School Grade Point Average,t=4.263

p=0.000 and p<0.05

High School Grade Point Average is significant.

For College Grade Point Average,t=8.540 p=0.00

p<0.05

College Grade Point Average is significant variable.

Coeffiiecient of determiantion=R sq=0.806

80.6% variation inScore on Stat Final is explained by 3 IV's

Number of Math Courses taken, High School Grade Point Average, College Grade Point Average.

Good model.

Final regression eq is

From output

Score on Stat Final=-8.251+5.095*High School Grade Point Average+9.915*College Grade Point Average

+2.901*Number of Math courses taken.