A statistical program is recommended. Consider the following data for a dependent variable y and two independent variables, x, and x₂ 30 12 94 47 10 108 25 17 112 51 16 178 51 19 175 74 7 170 36 12 117 59 13 142 76 16 211 (a) Develop an estimated regression equation relating y to x₁- (Round your numerical values to one decimal place.) Predict y if x₂-51. (Round your answer to one decimal place.) (b) Develop an estimated regression equation relating y to x₂ (Round your numerical values to one decimal place.) Predict y if x₂-16. (Round your answer to one decimal place.) (c) Develop an estimated regression equation relating y tox, and x₂. (Round your numerical values to one decimal place.) Predict y if x₂ - 51 and x₂ 16. (Round your answer to one decimal place.)

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### Regression Analysis with Multiple Variables

A statistical program is recommended.

Consider the following data for a dependent variable \( y \) and two independent variables, \( x_1 \) and \( x_2 \):

| \( x_1 \) | \( x_2 \) | \( y \)  |
|------- |------- |-----|
| 30     | 94     | 148 |
| 20     | 49     | 108 |
| 25     | 17     | 112 |
| 45     | 59     | 174 |
| 40     | 95     | 191 |
| 50     | 112    | 204 |
| 74     | 112    | 273 |
| 49     | 32     | 149 |
| 39     | 12     | 117 |
| 55     | 16     | 211 |

#### Task (a): Develop an Estimated Regression Equation for \( y \) Relating to \( x_1 \)
(Round your numerical values to one decimal place.)

\[ \hat{y} = \]

**Predict \( y \) if \( x_1 = 51 \).** (Round your answer to one decimal place.)

\[ \hat{y} = \]

#### Task (b): Develop an Estimated Regression Equation for \( y \) Relating to \( x_2 \)
(Round your numerical values to one decimal place.)

\[ \hat{y} = \]

**Predict \( y \) if \( x_2 = 16 \).** (Round your answer to one decimal place.)

\[ \hat{y} = \]

#### Task (c): Develop an Estimated Regression Equation for \( y \) Relating to \( x_1 \) and \( x_2 \)
(Round your numerical values to one decimal place.)

\[ \hat{y} = \]

**Predict \( y \) if \( x_1 = 51 \) and \( x_2 = 16 \).** (Round your answer to one decimal place.)

\[ \hat{y} = \]

**Explanation of Diagram:**
The table above consists of three columns: \( x_1 \), \( x_2 \), and \( y \). Each row represents an observation, denoting the values of the independent variables \( x_1 \) and \( x_2 \),
Transcribed Image Text:### Regression Analysis with Multiple Variables A statistical program is recommended. Consider the following data for a dependent variable \( y \) and two independent variables, \( x_1 \) and \( x_2 \): | \( x_1 \) | \( x_2 \) | \( y \) | |------- |------- |-----| | 30 | 94 | 148 | | 20 | 49 | 108 | | 25 | 17 | 112 | | 45 | 59 | 174 | | 40 | 95 | 191 | | 50 | 112 | 204 | | 74 | 112 | 273 | | 49 | 32 | 149 | | 39 | 12 | 117 | | 55 | 16 | 211 | #### Task (a): Develop an Estimated Regression Equation for \( y \) Relating to \( x_1 \) (Round your numerical values to one decimal place.) \[ \hat{y} = \] **Predict \( y \) if \( x_1 = 51 \).** (Round your answer to one decimal place.) \[ \hat{y} = \] #### Task (b): Develop an Estimated Regression Equation for \( y \) Relating to \( x_2 \) (Round your numerical values to one decimal place.) \[ \hat{y} = \] **Predict \( y \) if \( x_2 = 16 \).** (Round your answer to one decimal place.) \[ \hat{y} = \] #### Task (c): Develop an Estimated Regression Equation for \( y \) Relating to \( x_1 \) and \( x_2 \) (Round your numerical values to one decimal place.) \[ \hat{y} = \] **Predict \( y \) if \( x_1 = 51 \) and \( x_2 = 16 \).** (Round your answer to one decimal place.) \[ \hat{y} = \] **Explanation of Diagram:** The table above consists of three columns: \( x_1 \), \( x_2 \), and \( y \). Each row represents an observation, denoting the values of the independent variables \( x_1 \) and \( x_2 \),
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