Question

Given below are seven observations collected in a regression study on two 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

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

Answer 1

Solution:

The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

  

The p-value is:

Now using technology like excel:

Conclusion: Since the p-value is less than the significance level 0.05, we, therefore, reject the null hypothesis and conclude that the slope is significantly different from zero