at is the value of the F test statistic (to 2 decimals)? Use Table 4 in Appendix B. at is the p-value? s than 0.01 ng a = 0.05, what is your conclusion? nclude the relationship is significant pose variables ₁ and 4 are dropped from the model and the following estimated regression equation is obtained. ŷ = 11.1-3.6x2 +8.123 this model SST = 1805 and SSR = 1,705. Compute SSE(#1, #2, T3, T4). (to 1 decimal, if necessary) Compute SSE(2, 3). (to 1 decimal, if necessary) Use an F test and a = 0.05 to determine whether #₁ and 4 contribute significantly to the model. at is the value of the F test statistic (to 2 decimals)? Use Table 4 in Appendix B. at is the p-value? s than 0.01 at is your conclusion about the two variables #1 and 4? nclude that these variables contribute significantly to the model ide Feedback "artially Correct Hir
at is the value of the F test statistic (to 2 decimals)? Use Table 4 in Appendix B. at is the p-value? s than 0.01 ng a = 0.05, what is your conclusion? nclude the relationship is significant pose variables ₁ and 4 are dropped from the model and the following estimated regression equation is obtained. ŷ = 11.1-3.6x2 +8.123 this model SST = 1805 and SSR = 1,705. Compute SSE(#1, #2, T3, T4). (to 1 decimal, if necessary) Compute SSE(2, 3). (to 1 decimal, if necessary) Use an F test and a = 0.05 to determine whether #₁ and 4 contribute significantly to the model. at is the value of the F test statistic (to 2 decimals)? Use Table 4 in Appendix B. at is the p-value? s than 0.01 at is your conclusion about the two variables #1 and 4? nclude that these variables contribute significantly to the model ide Feedback "artially Correct Hir
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### 16.2 Practice
**a.** Calculate the Mean Squared Error (MSE).
\[ \text{MSE} = \text{_____} \text{(to 2 decimals, if necessary)} \]
**Question: What is the value of the \( F \) test statistic (to 2 decimals)? Use Table 4 in Appendix B.**
\[ [ \text{Input field} ] \text{Incorrect response (X mark)} \]
**Question: What is the p-value?**
\[ \text{[Dropdown Menu]} \]
Options:
- less than 0.01 [✔️Correct]
- between 0.01 and 0.05
- between 0.05 and 0.10
- greater than 0.10
**Question: Using \( \alpha = 0.05 \), what is your conclusion?**
Options:
- Conclude the relationship is significant [✔️Correct]
- Do not conclude the relationship is significant
**Suppose variables \( x_1 \) and \( x_4 \) are dropped from the model and the following estimated regression equation is obtained:**
\[ \hat{y} = 11.1 - 3.6x_2 + 8.1x_3 \]
For this model:
SST = 1805 and SSR = 1,705.
**b. Compute SSE \( (x_1, x_2, x_3, x_4) \).**
\[ \text{SSE} = \text{_____} \text{(to 1 decimal, if necessary)} \]
\[ [ \text{Input field} ] \text{Incorrect response (X mark)} \]
**c. Compute SSE\( (x_2, x_3) \).**
\[ \text{SSE} = \text{_____} \text{(to 1 decimal, if necessary)} \]
\[ [ \text{Input field} ] \text{Incorrect response (X mark)} \]
**d. Use an \( F \) test and \( \alpha = 0.05 \) to determine whether \( x_1 \) and \( x_4 \) contribute significantly to the model.**
**Question: What is the value of the \( F \) test statistic (to 2 decimals)? Use Table 4 in Appendix B.**
\[ [](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52390996-0048-48b9-99d6-ecc2feddac1b%2Fa02e349b-0834-497b-86e2-fe89b052e157%2Fa45e0zs_processed.png&w=3840&q=75)
Transcribed Image Text:### 16.2 Practice
**a.** Calculate the Mean Squared Error (MSE).
\[ \text{MSE} = \text{_____} \text{(to 2 decimals, if necessary)} \]
**Question: What is the value of the \( F \) test statistic (to 2 decimals)? Use Table 4 in Appendix B.**
\[ [ \text{Input field} ] \text{Incorrect response (X mark)} \]
**Question: What is the p-value?**
\[ \text{[Dropdown Menu]} \]
Options:
- less than 0.01 [✔️Correct]
- between 0.01 and 0.05
- between 0.05 and 0.10
- greater than 0.10
**Question: Using \( \alpha = 0.05 \), what is your conclusion?**
Options:
- Conclude the relationship is significant [✔️Correct]
- Do not conclude the relationship is significant
**Suppose variables \( x_1 \) and \( x_4 \) are dropped from the model and the following estimated regression equation is obtained:**
\[ \hat{y} = 11.1 - 3.6x_2 + 8.1x_3 \]
For this model:
SST = 1805 and SSR = 1,705.
**b. Compute SSE \( (x_1, x_2, x_3, x_4) \).**
\[ \text{SSE} = \text{_____} \text{(to 1 decimal, if necessary)} \]
\[ [ \text{Input field} ] \text{Incorrect response (X mark)} \]
**c. Compute SSE\( (x_2, x_3) \).**
\[ \text{SSE} = \text{_____} \text{(to 1 decimal, if necessary)} \]
\[ [ \text{Input field} ] \text{Incorrect response (X mark)} \]
**d. Use an \( F \) test and \( \alpha = 0.05 \) to determine whether \( x_1 \) and \( x_4 \) contribute significantly to the model.**
**Question: What is the value of the \( F \) test statistic (to 2 decimals)? Use Table 4 in Appendix B.**
\[ [
![### Regression Analysis Practice
In a regression analysis involving 30 observations, the following estimated regression equation was obtained:
\[ \hat{y} = 17.6 + 3.8x_1 - 2.3x_2 + 7.6x_3 + 2.7x_4 \]
For this estimated regression equation, the Sum of Squares for Total (SST) is 1805 and the Sum of Squares for Regression (SSR) is 1748.
#### Part a:
At \(\alpha = 0.05\), test the significance of the relationship among the variables.
- Sum of Squares for Error (SSE): \( 57 \) (to 1 decimal, if necessary)
- Mean Square Regression (MSR): \( 437 \) (to 1 decimal, if necessary)
- Mean Square Error (MSE): ________ (to 2 decimals, if necessary)
What is the value of the \( F \) test statistic (to 2 decimals)? Use Table 4 in Appendix B.
\[ \text{What is the p-value?} \]
- Less than 0.01
Using \(\alpha=0.05\), what is your conclusion?
- **Conclusion:** Conclude the relationship is significant.
#### Part b:
Suppose variables \( x_1 \) and \( x_4 \) are dropped from the model and the following estimated regression equation is obtained:
\[ \hat{y} = 11.1 - 3.6x_2 + 8.1x_3 \]
For this model, SST = 1805 and SSR = 1705.
Compute Sum of Squares for Error (SSE) for \( (x_1, x_2, x_3, x_4) \).
________ (to 1 decimal, if necessary)
#### Part c:
Compute SSE for \( (x_2, x_3) \).
________ (to 1 decimal, if necessary)
#### Part d:
Use an \( F \) test and \(\alpha = 0.05\) to determine whether \(x_1\) and \(x_4\) contribute significantly to the model.
- What is the value of the \( F \) test statistic (to 2 decimals)? Use Table 4 in Appendix B.
\[ \text{What is the p-value?} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52390996-0048-48b9-99d6-ecc2feddac1b%2Fa02e349b-0834-497b-86e2-fe89b052e157%2Fxjeatg9_processed.png&w=3840&q=75)
Transcribed Image Text:### Regression Analysis Practice
In a regression analysis involving 30 observations, the following estimated regression equation was obtained:
\[ \hat{y} = 17.6 + 3.8x_1 - 2.3x_2 + 7.6x_3 + 2.7x_4 \]
For this estimated regression equation, the Sum of Squares for Total (SST) is 1805 and the Sum of Squares for Regression (SSR) is 1748.
#### Part a:
At \(\alpha = 0.05\), test the significance of the relationship among the variables.
- Sum of Squares for Error (SSE): \( 57 \) (to 1 decimal, if necessary)
- Mean Square Regression (MSR): \( 437 \) (to 1 decimal, if necessary)
- Mean Square Error (MSE): ________ (to 2 decimals, if necessary)
What is the value of the \( F \) test statistic (to 2 decimals)? Use Table 4 in Appendix B.
\[ \text{What is the p-value?} \]
- Less than 0.01
Using \(\alpha=0.05\), what is your conclusion?
- **Conclusion:** Conclude the relationship is significant.
#### Part b:
Suppose variables \( x_1 \) and \( x_4 \) are dropped from the model and the following estimated regression equation is obtained:
\[ \hat{y} = 11.1 - 3.6x_2 + 8.1x_3 \]
For this model, SST = 1805 and SSR = 1705.
Compute Sum of Squares for Error (SSE) for \( (x_1, x_2, x_3, x_4) \).
________ (to 1 decimal, if necessary)
#### Part c:
Compute SSE for \( (x_2, x_3) \).
________ (to 1 decimal, if necessary)
#### Part d:
Use an \( F \) test and \(\alpha = 0.05\) to determine whether \(x_1\) and \(x_4\) contribute significantly to the model.
- What is the value of the \( F \) test statistic (to 2 decimals)? Use Table 4 in Appendix B.
\[ \text{What is the p-value?} \]
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