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

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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

### 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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