In a regression analysis involving 30 observations, the following estimated regressionequation was obtained. y^ =17.6+3.8x 1 −2.3x 2 +7.6x 3 +2.7x 4​For this estimated regression equation SST = 1805 and SSR = 1760. a. At \alpha =α= .05, test the significance of the relationship among the variables. Suppose variables x 1 and x 4 are dropped from the model and the following estimatedregression equation is obtained. y^ =11.1−3.6x 2​ +8.1x 3For this model SST = 1805 and SSR = 1705.b. Compute SSE(x 1 ,x 2 ,x 3 ,x 4 )c. Compute SSE (x2 ,x3 ) d. Use an F test and a .05 level of significance to determine whether x1 and x4 contribute significantly to the model.

(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.

Hence, we reject the null hypothesis

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step-by-step explanation: