c) Does the addition of X significantly contribute to prediction of y after accounting for the contribution of X₂? Use=0.05- O Reject the null hypothesis O Do not reject the null hypothesis

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**SAS Output Analysis for Regressions**

This page provides an overview of how to analyze regression output using SAS for a random sample of size 20.

### Regression of \( y \) on \( x_1 \) and \( x_2 \)

- **Number of Observations Read:** 20
- **Number of Observations Used:** 20

#### Analysis of Variance Table

| Source  | DF | Sum of Squares | Mean Square | F Value | Pr > F  |
|---------|----|----------------|-------------|---------|---------|
| Model   | 2  | 1317.79841     | 658.89921   | 20.84   | <.0001  |
| Error   | 17 | 537.40359      | 31.61198    |         |         |
| Corrected Total | 19 | 1855.20200   |             |         |         |

#### Summary Statistics

- **R-Square:** 0.818318
- **Coefficient Variance:** 22.31297
- **Root MSE:** 4.589778
- **y Mean:** 20.57000

#### Parameter Estimates

| Parameter | Estimate   | Standard Error |
|-----------|------------|----------------|
| Intercept | -36.7649258| 7.01092577     |
| x1        | 0.00076294 | 0.00063630     |
| x2        | 1.19217421 | 0.56165391     |

#### Type I SS

| Source | SS        |
|--------|-----------|
| x1     | 1.352481  |
| x2     | 1309.445931|

#### Type III SS

| Source | SS        |
|--------|-----------|
| x1     | 30.2855361|
| x2     | 94.9129162|

### Regression of \( y \) on \( x_1, x_2, \) and \( x_3 \)

#### Analysis of Variance Table

| Source  | DF | Sum of Squares | Mean Square | F Value | Pr > F  |
|---------|----|----------------|-------------|---------|---------|
| Model   | 3  | 1519.144491    | 506.048114  | 24
Transcribed Image Text:**SAS Output Analysis for Regressions** This page provides an overview of how to analyze regression output using SAS for a random sample of size 20. ### Regression of \( y \) on \( x_1 \) and \( x_2 \) - **Number of Observations Read:** 20 - **Number of Observations Used:** 20 #### Analysis of Variance Table | Source | DF | Sum of Squares | Mean Square | F Value | Pr > F | |---------|----|----------------|-------------|---------|---------| | Model | 2 | 1317.79841 | 658.89921 | 20.84 | <.0001 | | Error | 17 | 537.40359 | 31.61198 | | | | Corrected Total | 19 | 1855.20200 | | | | #### Summary Statistics - **R-Square:** 0.818318 - **Coefficient Variance:** 22.31297 - **Root MSE:** 4.589778 - **y Mean:** 20.57000 #### Parameter Estimates | Parameter | Estimate | Standard Error | |-----------|------------|----------------| | Intercept | -36.7649258| 7.01092577 | | x1 | 0.00076294 | 0.00063630 | | x2 | 1.19217421 | 0.56165391 | #### Type I SS | Source | SS | |--------|-----------| | x1 | 1.352481 | | x2 | 1309.445931| #### Type III SS | Source | SS | |--------|-----------| | x1 | 30.2855361| | x2 | 94.9129162| ### Regression of \( y \) on \( x_1, x_2, \) and \( x_3 \) #### Analysis of Variance Table | Source | DF | Sum of Squares | Mean Square | F Value | Pr > F | |---------|----|----------------|-------------|---------|---------| | Model | 3 | 1519.144491 | 506.048114 | 24
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