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In exercise $1,$ the following estimated regression equation based on 10 observations waspresented.$$\hat{y}=29.1270+.5906 x_{1}+.4980 x_{2}$$Here SST $=6724.125,$ SSR $=6216.375, s_{b_{1}}=.0813,$ and $s_{b_{2}}=.0567$$\begin{array}{l}{\text { a. Compute MSR and MSE. }} \\ {\text { b. Compute } F \text { and perform the appropriate } F \text { test. Use } \alpha=.05} \\ {\text { c. Perform at test for the significance of } \beta_{1} . \text { Use } \alpha=.05} \\ {\text { d. Perform a } t \text { test for the significance of } \beta_{2} . \text { Use } \alpha=.05}\end{array}$

a) 72.5357b) 42.85c) 7.2645d) 8.7831

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

University of North Carolina at Chapel Hill

University of St. Thomas

Idaho State University

Boston College

Lectures

0:00

07:48

Refer to the data presente…

Okay, so we know that I'm as are just equal to us, are Okay. Inches 6216. Closer to she's got three dozen. No, that s P is equal to just S S T miners. That's our which is 24 from 1 to 5 minus exciting tour in 16 which will give us seven. We knew that Muskie s e over on my skin. Just one, which is 7.7. Should give us 72 5357 kids. I know in part B, you know, just be on this are over E, which will give us 3100 1875 my over 72 55 one Rich is gonna give us 42 point 85 years for no. We can calculate critical you, which is just gonna be 4.73 74 5%. So sheer. We know because the F value is greater than critical value. We know that we can reject. We're alternative. There are no buses. Therefore, we can conclude that the regression coefficient is the best fit to get data moving. See a test statistic T Is he cool to be one. Thus be one which is equal to 0.59 six over is your values To get 7.265 It's a critical value of T equals 2.306 at 5%. Therefore, since the T value is better, then the critical value just a critical values this insistence crater begin therefore rejected the bill. What's is and concluded population regression coefficient of X one is not equal to zero is significant. Deve, Find a tested just again for SP two. Just your 498 over your prints. You 56 give us 8.7. Do you critical value g easier. Six at 5%. So here, since the T value is getting a critical value again, we reject. No, I thought says we conclude that the population regression coefficient of X two is significant. Nautical to do

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