In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ = 25.2 + 5.5x₁ For this estimated regression equation SST = 1,525 and SSE = 520. (a) Ata = 0.05, test whether x₁ is significant. (b) Suppose that variables x₂ and x3 are added to the model and the following regression equation is obtained. ŷ = 16.3 +2.3x₁ + 12.1x₂ - 5.8x3 For this estimated regression equation SST = 1,525 and SSE = 100. Use an F test and a 0.05 level of significance to determine whether x₂ and x3 contribute significantly to the model.
In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ = 25.2 + 5.5x₁ For this estimated regression equation SST = 1,525 and SSE = 520. (a) Ata = 0.05, test whether x₁ is significant. (b) Suppose that variables x₂ and x3 are added to the model and the following regression equation is obtained. ŷ = 16.3 +2.3x₁ + 12.1x₂ - 5.8x3 For this estimated regression equation SST = 1,525 and SSE = 100. Use an F test and a 0.05 level of significance to determine whether x₂ and x3 contribute significantly to the model.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![Since a new regression equation with extra variables was fit to the same data, the value of the F test statistic will be calculated as follows. The value of SSR(full) is the sum of squares due to regression of the model with the extra variables, SSR(reduced) is the sum of squares due to regression for the original model, the number of extra terms refers to the number of extra variables in the new model, and MSE(full) is the mean square error of the model with the extra variables.
\[ F = \frac{\text{SSE(reduced)} - \text{SSE(full)}}{\text{number of extra terms}} \div \text{MSE(full)} \]
The original model was \( \hat{y} = 25.2 + 5.5x_1 \) and the new model is \( \hat{y} = 16.3 + 2.3x_1 + 12.1x_2 - 5.8x_3 \). The new model added terms \( x_2 \) and \( x_3 \), so there are \( \boxed{2} \) extra terms.
Recall that the value of the SSE for the original (reduced) model was given to be 520, so we have
\[ \text{SSE(reduced)} = \boxed{260} \]
There are no graphs or diagrams in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7b76bbb-1122-4c75-9c9e-2038b7c47d4e%2F61f1351e-72b6-43e1-93fe-57c798f6a3b5%2Fvhsyt5a_processed.png&w=3840&q=75)
Transcribed Image Text:Since a new regression equation with extra variables was fit to the same data, the value of the F test statistic will be calculated as follows. The value of SSR(full) is the sum of squares due to regression of the model with the extra variables, SSR(reduced) is the sum of squares due to regression for the original model, the number of extra terms refers to the number of extra variables in the new model, and MSE(full) is the mean square error of the model with the extra variables.
\[ F = \frac{\text{SSE(reduced)} - \text{SSE(full)}}{\text{number of extra terms}} \div \text{MSE(full)} \]
The original model was \( \hat{y} = 25.2 + 5.5x_1 \) and the new model is \( \hat{y} = 16.3 + 2.3x_1 + 12.1x_2 - 5.8x_3 \). The new model added terms \( x_2 \) and \( x_3 \), so there are \( \boxed{2} \) extra terms.
Recall that the value of the SSE for the original (reduced) model was given to be 520, so we have
\[ \text{SSE(reduced)} = \boxed{260} \]
There are no graphs or diagrams in the image.
![You may need to use the appropriate technology to answer this question.
In a regression analysis involving 27 observations, the following estimated regression equation was developed.
\[
\hat{y} = 25.2 + 5.5x_1
\]
For this estimated regression equation SST = 1,525 and SSE = 520.
(a) At \(\alpha = 0.05\), test whether \(x_1\) is significant.
(b) Suppose that variables \(x_2\) and \(x_3\) are added to the model and the following regression equation is obtained.
\[
\hat{y} = 16.3 + 2.3x_1 + 12.1x_2 - 5.8x_3
\]
For this estimated regression equation SST = 1,525 and SSE = 100.
Use an F test and a 0.05 level of significance to determine whether \(x_2\) and \(x_3\) contribute significantly to the model.
**Step 1**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7b76bbb-1122-4c75-9c9e-2038b7c47d4e%2F61f1351e-72b6-43e1-93fe-57c798f6a3b5%2Fue70isr_processed.png&w=3840&q=75)
Transcribed Image Text:You may need to use the appropriate technology to answer this question.
In a regression analysis involving 27 observations, the following estimated regression equation was developed.
\[
\hat{y} = 25.2 + 5.5x_1
\]
For this estimated regression equation SST = 1,525 and SSE = 520.
(a) At \(\alpha = 0.05\), test whether \(x_1\) is significant.
(b) Suppose that variables \(x_2\) and \(x_3\) are added to the model and the following regression equation is obtained.
\[
\hat{y} = 16.3 + 2.3x_1 + 12.1x_2 - 5.8x_3
\]
For this estimated regression equation SST = 1,525 and SSE = 100.
Use an F test and a 0.05 level of significance to determine whether \(x_2\) and \(x_3\) contribute significantly to the model.
**Step 1**
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