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In a regression analysis involving 30 observations, the following estimated regressionequation was obtained.$$\hat{y}=17.6+3.8 x_{1}-2.3 x_{2}+7.6 x_{3}+2.7 x_{4}$$a. Interpret $b_{1}, b_{2}, b_{3},$ and $b_{4}$ in this estimated regression equation.b. Predict $y$ when $x_{1}=10, x_{2}=5, x_{3}=1,$ and $x_{4}=2 .$

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a. $y$ increases, on average, by 3.8 per unit of $x_{1}$ .$y$ decreases, on average, by 2.3 per unit of $x_{2}$ .$y$ increases, on average, by 7.6 per unit of $x_{3}$ .$y$ increases, on average, by 2.7 per unit of $x_{4}$ .b. 57.1

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Piedmont College

Oregon State University

University of St. Thomas

Lectures

0:00

The estimated regression e…

09:55

1. The estimated regressio…

02:12

In exercise $1,$ the follo…

Given are five observation…

So this is a question involving multiple regression, and the multiple regression equation we're given is why Had two Sequels to 17.6 was 3.8 x one minus 2.3 x two plus 7.6 x three plus 2.7 x four So here we have this equation is obtained from 30 observations, and we basically have all off the estimated parameters here, which is typical for our multiple regression equation pp exp And in the first part, we are asked to interpret B one, b two, B three and B four So B one, B two, B three and before in this equation. So let's go ahead and do that. So first, let's take B one. So be one is 3.8, so be one basically represents change in why an increase in why off 3.8 when there is an increase in one unit off X one provided all the variables. All the other variables are constant, so provided the next two x three and x four are constant now beat too, which is minus 2.3. It's an average decrease in why by 2.3 when there's an increase in one unit off X two, provided x one x three and x four are all constant. Okay, B three, which is plus 7.6, is an increase in why by 7.6 when there is an increase in one unit off X three provided x two x one and x four are old constant before, which is 2.7. It's an increase in why, by an average of 2.7, when there's a one unit increase off x four, provided that x one x two x three are all constant. So this it's our answer to part. Hey, now let's move on to part B So in part being were asked to predict why when x one is equals. To tell X two use equals to five X three is one and X four is too. So let's substitute all off the values back into this equation and soft. So are predicted value off. Why you see cool to 17 0.6 plus 3.8 x one minus 2.3 Next to plus 7.6 x three yes 2.7 x four, which gives us 57 0.1 which is our answer to party. So substituting all the values we get wise equals to 57.1.

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