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In exercise $2,10$ observations were provided for a dependent variable $y$ and two indepen-dent variables $x_{1}$ and $x_{2} ;$ for these data $S S T=15,182.9$ and $S S R=14,052.2 .$$\begin{array}{l}{\text { a. Compute } R^{*} \text { . }} \\ {\text { b. Compute } R_{\mathrm{a}}^{2} \text { . }} \\ {\text { c. Does the estimated regression equation a large amount of the variability in the }} \\ {\text { data? Explain. }}\end{array}$

a. 0.926b. 0.905c. 90.5$\%$ of the variability in $y$ has been explained by the regressionequation.

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Missouri State University

Piedmont College

Cairn University

Oregon State University

Lectures

0:00

03:39

In exercise $4,$ the follo…

03:22

In exercise I, the followi…

So in this question, we are given the total sum of squares SST and were also given S S r and were asked to calculate R squared for the coefficient off multiple regression equation. So our square we know from our formula this s car over s team. So we're gonna put in the values 14 52.2 over 15, 182 0.9. So that gives us a value of R squared off 0.92 by five. Rounded to three decimal places is 0.926 This is our answer. Took part A in part B were as to compute the adjusted multiple regression coefficient off determination. So for that, we just have to adjust our formula a little bit. So our formula for R a squared is one minus one minus R squared and minus one over and minus P minus one. Where n is the number of observations and P iss the number of independent variables. So we're going to substitute that in, So we're basically going to get one minus one minus car squared, which we have from part a and minus one over n minus, P minus one, which gives us 0.905 which is our answer to party for the adjusted R squared, which is slightly less than our our square. How important, See, were asked if the estimated regression equation explains for a large amount off variability. So we see here that are adjusted. Value off R squared is pretty large is actually 90.5%. So yes, the equation. Just explain large amount off the variability because the amount of variability explained ISS 90.5 percent. So yes, because the amount of variability explained is large.

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