Answer:
(a) There is a significant relationship between y and
(b)
(c)
(d) and are significant
Step-by-step explanation:
Given
--- estimated regression equation
--- independent variables i.e. x1 to x4
Solving (a): Test of significance
We have:
There is no significant relationship between y and
There is a significant relationship between y and
First, we calculate the t-score using:
Next, we calculate the p value from the t score
Where:
The p value when and is:
So:
i.e.
Solving (b):
To calculate SSE, we use:
Given that:
-----------
So:
Solving (c):
To calculate SSE, we use:
Given that:
-----------
So:
Solving (d): F test of significance
The null and alternate hypothesis are:
We have:
and are not significant
and are significant
For this model:
Calculate the t-score
Next, we calculate the p value from the t score
Where:
The p value when and is:
So:
i.e.
<em>Hence, we reject the null hypothesis</em>