Question

Suppose you are given the following x and y values. Assume x is the independent variable and y the dependent variable.

x	y
13	10
10	11
3	4
29	23
5	8
25	21
8	10
17	15
19	17
31	29
23	24

Is there a significant relationship between x and y? Explain. Test at a 5% level of significance

A. Yes, since the null hypothesis H0: β1 = 0 is not rejected.

B. No, since the null hypothesis H0: β1 = 0 is not rejected.

C. No, since the null hypothesis H0: β1 = 0 is rejected.

D. Yes, since the null hypothesis H0: β1 = 0 is rejected.

What is the regression equation?

A. 2.5296 + 0.7878x

B. 2.5296 + 0.7878y

C. 2.5296x + 0.7878

D. 0.7878x

What is the coefficient of determination?

A. 11.9696

B. 2.006

C. 0.0000

D. 0.9409

Answer 1

The statistical software output for this problem is:

Hence,

Answer - 1: The relationship is significant since the null hypothesis H0: β1 = 0 is rejected.

Option D is correct.

Answer - 2: Regression equation:

y = 2.5296 + 0.7878x

Option A is correct.

Answer - 3: Coefficient of determination = R - square = 0.9409

Option D is correct.