MATLAB: An Introduction with Applications
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,
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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,
**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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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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