Question

(a) Using the above t-test data to determine whether or not there is a linear relationship between the two variables.
(b) Using the above ANOVA F-test data to determine whether or not there is a linear relationship between the two variables.
(c) How do the results in (a) compare to those in (b)?

Answer 1

a) Null Hypothesis H0: $\beta 1=0$

ALTERNATIVE HYPOTHESIS Ha: $\beta 1\ne 0$

alpha=0.01

t= 3.040

P value= 0.00292

Since P value <0.01 therefore SIGNIFICANT.

Decision: REJECT H0.

Conclusion: We can conclude that there is relationship between two variables.

b) From Anova table

F= t^2= 9.2402

P value= 0.00292

Since P <0.01 level of significance.

Decision: Reject H0.

Conclusion: We have sufficient evidence to conclude that there is linear relation between two variables.

c) F statistic is square of t statistic.

So F= t^2= 9.2402