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In exercise $3,$ the following estimated regression equation based on 30 observations waspresented.$$\hat{y}=17.6+3.8 x_{1}-2.3 x_{2}+7.6 x_{3}+2.7 x_{4}$$$\begin{array}{l}{\text { The values of SST and SSR are } 1805 \text { and } 1760 \text { , respectively. }} \\ {\text { a. Compute } R^{2} .} \\ {\text { b. Compute } R_{3}^{2} \text { . }} \\ {\text { c. Comment on the goodness of fit. }}\end{array}$

a. 0.9751b. 0.9711c. Good fit

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Missouri State University

Piedmont College

Oregon State University

Idaho State University

Lectures

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The data from exercise 2 f…

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In exercise $1,$ the follo…

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For the following exercise…

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Refer to the data presente…

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(a) Compute the power regr…

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So in this question, we are given the equation Over here. We're told that the equation had 30 observations, and we see that the equation has or independent variables were given the value of the some off total sum of squares and the sum of squares due to regression and in part A were as to compute r squared. So we know our squared is to sum of squares due to regression over the total sum of squares. So that's 17 60/18 or five, which gives us 0.9751 And that's our answer to Part eight now, in part being whereas to compute adjusted R squared. So let's write the formula for the adjusted R squared. So we have one minus one minus R squared 10 minus one over n minus, P minus one. So we have our adjusted r squared R squared over here from party, and we have N and P. So we're going to substitute that we have one minus one minus 0.9751 29/30 minus yeah, which is 26 minus 1 20 five. So adjusted R squared is 0.9711 and That's our answer to part Pete now in Part C. We're as to comment on the goodness off fit. So to comment on the goodness of fit. We look at our adjusted value of r squared, and we see that since our squareness equals 2.9711 97.1% off, the variability explained by the equation. And so it's basically a large percentage of the variability is explained by the equation. So the equation does give us a good fit. That's our answer to part C.

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