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MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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How do I find the p-value to each corresponding test statistic to complete the ANOVA table? I also need help with parts b-d.
![The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high-school GPA.
\[ \hat{y} = -1.41 + 0.0235x_1 + 0.00486x_2 \]
where
\( x_1 = \) high-school grade point average
\( x_2 = \) SAT mathematics score
\( y = \) final college grade point average
Round test statistic values to 2 decimal places and all other values to 4 decimal places. Do not round your intermediate calculations.
a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers.
**SUMMARY OUTPUT**
**Regression Statistics**
| Statistics | Value |
|-------------------|--------|
| Multiple R | 0.9681 |
| R Square | 0.9373 |
| Adjusted R Square | 0.9194 |
| Standard Error | 0.1296 |
| Observations | 10 |
**ANOVA**
| Source | df | SS | MS | F | Significance F |
|--------------|----|--------|-------|------|----------------|
| Regression | 2 | 1.76209| 0.8810| 52.31| 0.0001 |
| Residual | 7 | 0.1179 | 0.0168| | |
| Total | 9 | 1.88 | | | |
**Coefficients**
| Coefficients | Standard Error | t Stat | P-value |
|--------------|----------------|--------|---------|
| Intercept | -1.4053 | 0.4848 | -2.90 | |
| X1 | 0.023467 | 0.0086666 | 2.71 | |
| X2 | 0.00486 | 0.001077 | 4.51 | |
b. Using \( \alpha = 0.05 \), test for overall significance.
- Select your answer -
**Explanation of Graphs/Tables:**
1. **Regression Statistics Table:**
- This table provides key statistics that describe the fit of the regression model. The Multiple R represents the correlation coefficient,](https://content.bartleby.com/qna-images/question/398dd4ea-d707-4cf3-85e2-b0229fb2dea0/bd643d37-51d0-4742-b690-b2de5efb5bdd/lfsbqx2_thumbnail.png)
Transcribed Image Text:The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high-school GPA.
\[ \hat{y} = -1.41 + 0.0235x_1 + 0.00486x_2 \]
where
\( x_1 = \) high-school grade point average
\( x_2 = \) SAT mathematics score
\( y = \) final college grade point average
Round test statistic values to 2 decimal places and all other values to 4 decimal places. Do not round your intermediate calculations.
a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers.
**SUMMARY OUTPUT**
**Regression Statistics**
| Statistics | Value |
|-------------------|--------|
| Multiple R | 0.9681 |
| R Square | 0.9373 |
| Adjusted R Square | 0.9194 |
| Standard Error | 0.1296 |
| Observations | 10 |
**ANOVA**
| Source | df | SS | MS | F | Significance F |
|--------------|----|--------|-------|------|----------------|
| Regression | 2 | 1.76209| 0.8810| 52.31| 0.0001 |
| Residual | 7 | 0.1179 | 0.0168| | |
| Total | 9 | 1.88 | | | |
**Coefficients**
| Coefficients | Standard Error | t Stat | P-value |
|--------------|----------------|--------|---------|
| Intercept | -1.4053 | 0.4848 | -2.90 | |
| X1 | 0.023467 | 0.0086666 | 2.71 | |
| X2 | 0.00486 | 0.001077 | 4.51 | |
b. Using \( \alpha = 0.05 \), test for overall significance.
- Select your answer -
**Explanation of Graphs/Tables:**
1. **Regression Statistics Table:**
- This table provides key statistics that describe the fit of the regression model. The Multiple R represents the correlation coefficient,
.**
For \( \beta_1 \), the p-value is - Select your answer - , so - Select your answer - \( H_0: \beta_1 = 0 \).
For \( \beta_2 \), the p-value is - Select your answer - , so - Select your answer - \( H_0: \beta_2 = 0 \).](https://content.bartleby.com/qna-images/question/398dd4ea-d707-4cf3-85e2-b0229fb2dea0/bd643d37-51d0-4742-b690-b2de5efb5bdd/rykgeol_thumbnail.png)
Transcribed Image Text:**c. Did the estimated regression equation provide a good fit to the data? Explain.**
- Select your answer - , because the \( R^2_a \) value is - Select your answer - than 0.50.
**d. Use the t test and \( \alpha = 0.05 \) to test \( H_0: \beta_1 = 0 \) and \( H_0: \beta_2 = 0 \). Use [t table](#).**
For \( \beta_1 \), the p-value is - Select your answer - , so - Select your answer - \( H_0: \beta_1 = 0 \).
For \( \beta_2 \), the p-value is - Select your answer - , so - Select your answer - \( H_0: \beta_2 = 0 \).
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