Question

Consider the following set of ordered pairs.

x 6 0 3 4 4 1

y 4 1 4 5 6 7

Assuming that the regression equation is y with caret = 3.750 + 0.250x and that the SSE = 20.0000​, test to determine if the slope is not equal to zero using alpha = 0.10.

a.) state the hypotheses

b.) what is the test statistic?

c.) what is the p value?

d.) state the conclusion

Answer 1

a)

null hypothesis: Ho:               β1		=	0
Alternate Hypothesis: Ha: β1		≠	0

b)

	s2 =SSE/(n-2)=	5.0000
std error σ              =	=se =√s2=	2.2361

estimated std error of slope =se(β1) =s/√Sxx=			0.4564
test stat t =	(bo-β1)/se(β1)=0.25/0.4564	=	0.5477

c)

from excel: p value =tdist(0.5477,6-2,2) =0.6130

d)

since p value >0.10 , we can not reject null hypothesis

we do not have sufficient evidence at 0.10 level to conclude that slope is different from zero .