Consider the following data for a dependent variable y and two independent variables, 1 and 22. X2 29 13 95 47 10 109 25 18 113 51 16 178 T 40 6 94 52 20 175 75 7 170 37 12 117 14 142 77 16 211 Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary. a. Develop an estimated regression equation relating y to 1. ŷ = + Predict y if a₁ = 35, ŷ y = b. Develop an estimated regression equation relating y to 2. ŷ = + X2 Predict y if *2 = 15. ŷ c. Develop an estimated regression equation relating y to 1 and 22. ŷ = x1 + Predict y if #₁ = 35 and 2 = 15. #1 y = + X2 x1 59

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter4: Equations Of Linear Functions
Section: Chapter Questions
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### Regression Analysis with Dependent and Independent Variables

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

\[
\begin{array}{ccc}
x_1 & x_2 & y \\
\hline
29 & 13 & 95 \\
47 & 10 & 109 \\
25 & 18 & 113 \\
51 & 16 & 178 \\
40 & 6 & 94 \\
52 & 20 & 175 \\
75 & 7 & 170 \\
37 & 12 & 117 \\
59 & 14 & 142 \\
77 & 16 & 211 \\
\end{array}
\]

Round all your answers to two decimal places. Enter negative values as negative numbers, if necessary.

#### a. Develop an estimated regression equation relating \( y \) to \( x_1 \).

\[
\hat{y} = \_\_\_\_\_\_\_\_\_\_ + \_\_\_\_\_\_\_\_\_\_ x_1
\]

**Predict \( y \) if \( x_1 = 35 \).**

\[
\hat{y} = \_\_\_\_\_\_\_
\]

#### b. Develop an estimated regression equation relating \( y \) to \( x_2 \).

\[
\hat{y} = \_\_\_\_\_\_\_\_\_\_ + \_\_\_\_\_\_\_\_\_\_ x_2
\]

**Predict \( y \) if \( x_2 = 15 \).**

\[
\hat{y} = \_\_\_\_\_\_\_
\]

#### c. Develop an estimated regression equation relating \( y \) to \( x_1 \) and \( x_2 \).

\[
\hat{y} = \_\_\_\_\_\_\_\_\_\_ + \_\_\_\_\_\_\_\_\_\_ x_1 + \_\_\_\_\_\_\_\_\_\_ x_2
\]

**Predict \( y \) if \( x_1 = 35 \) and \( x_2 = 15 \).**

\[
\hat{y} = \_\_\_\_\_\_\_
\]
Transcribed Image Text:### Regression Analysis with Dependent and Independent Variables Consider the following data for a dependent variable \( y \) and two independent variables, \( x_1 \) and \( x_2 \). \[ \begin{array}{ccc} x_1 & x_2 & y \\ \hline 29 & 13 & 95 \\ 47 & 10 & 109 \\ 25 & 18 & 113 \\ 51 & 16 & 178 \\ 40 & 6 & 94 \\ 52 & 20 & 175 \\ 75 & 7 & 170 \\ 37 & 12 & 117 \\ 59 & 14 & 142 \\ 77 & 16 & 211 \\ \end{array} \] Round all your answers to two decimal places. Enter negative values as negative numbers, if necessary. #### a. Develop an estimated regression equation relating \( y \) to \( x_1 \). \[ \hat{y} = \_\_\_\_\_\_\_\_\_\_ + \_\_\_\_\_\_\_\_\_\_ x_1 \] **Predict \( y \) if \( x_1 = 35 \).** \[ \hat{y} = \_\_\_\_\_\_\_ \] #### b. Develop an estimated regression equation relating \( y \) to \( x_2 \). \[ \hat{y} = \_\_\_\_\_\_\_\_\_\_ + \_\_\_\_\_\_\_\_\_\_ x_2 \] **Predict \( y \) if \( x_2 = 15 \).** \[ \hat{y} = \_\_\_\_\_\_\_ \] #### c. Develop an estimated regression equation relating \( y \) to \( x_1 \) and \( x_2 \). \[ \hat{y} = \_\_\_\_\_\_\_\_\_\_ + \_\_\_\_\_\_\_\_\_\_ x_1 + \_\_\_\_\_\_\_\_\_\_ x_2 \] **Predict \( y \) if \( x_1 = 35 \) and \( x_2 = 15 \).** \[ \hat{y} = \_\_\_\_\_\_\_ \]
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b and c are all wrong. please do them correct.

 

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