## Related questions with answers

The data is below:

$\begin{array}{r|rrrrr} x_i & 2 & 6 & 9 & 13 & 20 \\ \hline y_i & 7 & 18 & 9 & 26 & 23 \end{array}$

The estimated regression equation for these data is $\hat{y}=7.6+.9 x$. What percentage of the total sum of squares can be accounted for by the estimated regression equation? What is the value of the sample correlation coefficient?

Solution

VerifiedFor this exercise, we are to determine the coefficient of determination and the sample correlation coefficient for the given table below

$\text{\small{Table 1. Given data}}.$

$\def\arraystretch{1.5} \begin{array}{c:ccccc} x_i & 2 & 6 & 9 & 13 & 20 \\ \hline y_i & 7 & 18 & 9 & 26 & 23 \\ \end{array}$

with an estimated regression equation:

$\hat y = 7.6 + 0.9x$

*What is the definition of the coefficient of determination $r^2$?*

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