Question

Below are 7 observations collected in a regression study on 2 variables, x (independent variable) and y (dependent variable).

x y

2 12

3 9

6 8

7 7

8 6

7 5

9 2

Given the followings

b1 = -1.13

SSR = 50.625

SSE= 9.376

Sb1 = .2165

At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. DONT USE EXCEL.

Answer 1

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

here degree of freedom =n-2=7-2 =5

for 5 df and 0.05 level ; critical value t =2.571

Decision rule: reject Ho if t<-2.571 or t >2.571

test statistic t =b1/Sb1=-1.13/0.2165 = -5.219

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that slope is significantly different from zero.