Question

Homework to be checked and reviewed for correctness.

The following data was collected for linear regression analysis. Becky wants to use shoe size to predict a person's GPA.

Shoe Size	6	11	5	10	8	9	12	6.5	7.5
GPA	2.1	2.9	4	3	1.5	2.4	3.5	1.98	3.88

A. Find r, using your calculator.

B) Do a hypothesis test on whether there is significant linear correlation?    a = 0.01 When you find the test statistic, find it by hand using the appropriate t formula.

C) Let GPA be the dependent variable; Using your calculator, give the regression equation.

D) Predict the GPA of a person with a shoe size of 7. Is this prediction valid according to the results of the hypothesis test in part b? EXPLAIN.

Answer 1

Ans:

a)

Correlation coefficient,r=0.095

b)n=9

Test statistic:

t=0.095*sqrt((9-2)/(1-0.095^2))

t=0.252

df=9-2=7

p-value=tdist(0.252,7,2)=0.8083

As,p-value>0.01,we fail to reject H0 and conclude that there is not significant linear correlation.

c)

Regression equation:

y'=0.0353 x+2.5127

d)

when shoe size=7

predicted GPA=0.0353*7+2.5127=2.7598

It is not a valid prediction,as linear correlation is not significant in part b.