The estimated regression equation for a model involving two independent variables and 10 observations follows. ý = 22.1370 + 0.5303Xq + 0.4920Xz (a) Interpret b, in this estimated regression equation. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. Ob₁ = = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. O b₁ = 22.1370 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. Ob ₁ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₁ = = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. Interpret b₂ in this estimated regression equation. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₂ is held constant. O b₂ = 22.1370 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. 05203 is an chang ant

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## Understanding the Estimated Regression Equation

The estimated regression equation for a model involving two independent variables and 10 observations is given by:

\[
\hat{y} = 22.1370 + 0.5303x_1 + 0.4920x_2
\]

### (a) Interpretation of Coefficients

**Interpret \( b_1 \) in this estimated regression equation:**

- \( b_1 = 0.5303 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_1 \) when \( x_2 \) is held constant.
- \( b_1 = 0.5303 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_1 \) is held constant.
- \( b_1 = 22.1370 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_2 \) is held constant.
- \( b_1 = 0.4920 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_1 \) is held constant.
- \( b_1 = 0.4920 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_1 \) when \( x_2 \) is held constant.

**Interpret \( b_2 \) in this estimated regression equation:**

- \( b_2 = 0.4920 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_1 \) is held constant.
- \( b_2 = 22.1370 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_2 \) is held constant.
- \( b_2 = 0.5303 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_1 \) when \( x_2 \) is held constant.
- \( b_2 = 0
Transcribed Image Text:## Understanding the Estimated Regression Equation The estimated regression equation for a model involving two independent variables and 10 observations is given by: \[ \hat{y} = 22.1370 + 0.5303x_1 + 0.4920x_2 \] ### (a) Interpretation of Coefficients **Interpret \( b_1 \) in this estimated regression equation:** - \( b_1 = 0.5303 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_1 \) when \( x_2 \) is held constant. - \( b_1 = 0.5303 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_1 \) is held constant. - \( b_1 = 22.1370 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_2 \) is held constant. - \( b_1 = 0.4920 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_1 \) is held constant. - \( b_1 = 0.4920 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_1 \) when \( x_2 \) is held constant. **Interpret \( b_2 \) in this estimated regression equation:** - \( b_2 = 0.4920 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_1 \) is held constant. - \( b_2 = 22.1370 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_2 \) when \( x_2 \) is held constant. - \( b_2 = 0.5303 \) is an estimate of the change in \( y \) corresponding to a 1 unit change in \( x_1 \) when \( x_2 \) is held constant. - \( b_2 = 0
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