Question

You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. You are given the following regression results, where the sample size is 10.,

	Coefficients	Standard Error
Intercept	-1.2	1
X	2	2

a) What is the value of the t test statistic?

b) At the α = 0.05 level of significance, what are the critical values?

c) Based on your answer to (a) and (b), what statistical decision should you make?

Answer 1

To test that there is no linear relationship between two variables, X and Y

H0 : = 0      i .e no linear relation ship between X & Y

vs

H1 : 0      i .e there is linear relationshp between two variables .

Failing to reject H0 implies that there is no linear relationship between X,Y

Test criteria : Reject H0 if T- Value = | to | >

                        where    to =  

                   and is t - table value

Total samples n =10

Regression equation will be

=_{0 + 1} X   = -1.2 + 2 * X

a)

value of the t test statistic will be given by ratio of intercept and its corresponding Standard Error

	Coefficients	Standard Error	T-Value
Intercept	-1.2	1	-1.2
X	2	2	1

b)

At the α = 0.05 level of significance, critical value is given by

Thus critical value is 2.306004 { t - table value at α = 0.05 , n=10 }

Here , to = = 2 / 2 = 1

                 = 2.306004

thus ,   1 < 2.306004

So | to | < , we will not reject H0 at 5% of level of significance .

c)

Based on (a) and (b), we conclude that there is no linear relationship between X ,Y