91Ó°ÊÓ

WE have been given a table

The linear correlation coefficient of given set of data

$r=\frac{∑x_i{y}_i−\frac{\left(∑x_i\right)\left(∑y_i\right)}{n}}{\sqrt{\left[∑x_i^2−{\left(∑x_i\right)}^2\right]\left[∑y_i^2−\frac{{\left(∑y_i\right)}^2}{n}\right]}}$

The value of correlation coefficient r suggests that there is a strong positive linear relationship

between size and price of custom homes .

The correlation coefficient ,r=0.829,suggestsastrong positive correlation between size and

price of custom homes

In particular, it indicates that as size of custom homes increases there is a strong tendency for

price of custom home to increase.

The graph from Exercise 14.90 is as follows

From the above graph also we can see that as size of custom homes increases there is a strong

tendency for price of custom home to increase.

Square of r is given by

From section 14.3(Exercise 14.52):

The mean of the observed tax efficiency is

$\begin{array}{r}SSR=∑{\left({\widehat{y}}_i−\stackrel{¯}{y}\right)}^2\\ =54565.76\\ SSR=∑{\left(y_i−\stackrel{¯}{y}\right)}^2\\ =79444.89\end{array}$

Coefficient of determination,

$\begin{array}{r}{\mathrm{r}}^2=\frac{SSR}{SST}\\ =\frac{54565.76}{79444.89}\\ =0.687\end{array}$

The value of,²is same in both methods