91Ó°ÊÓ

Given table is

We have to obtain the linear correlation coefficient.

The formula of correlation coefficient is

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

The appropriate value can be calculated in the below table

Therefore,

$$\begin{gathered} r=\frac{13168-\left(41\right)\left(3422\right)/10}{\sqrt{\left[199-(41{)}^2/10\right]\left[1196690-(3422{)}^2/10\right]}} \\ =-0.9679 \end{gathered}$$

The given table is

We have to interpret the value of $r$in terms of the linear relationship between the two variables in question.

The variables are strongly correlated if the estimated $r$is near to $Â\pm 1$

Close to $-1$is the computed correlation coefficient. As a result, the variables are negatively connected. As a result, as the age of the person increases, the price decreases.

The given table is

We have to discuss the graphical interpretation of the value of $r$and verify that it is consistent with the graph you obtained in the corresponding exercise in Section 4.2.

If $r$is near to $0$, the data points are essentially scattered along a horizontal line. If $r$is the father of $Â\pm 1$, the data points are more widely dispersed around the regression line. If $r$close to$-1$, the data points cluster closely around the regression line.

Graph is given below

$r$is close to $-1$when calculated. As a result, the data points are closely clustered around the regression line. The points in the graph are closely clustered around the regression line. As a result, the calculated correlation coefficient matches the graph.

The given table is

We have to square $r$and compare the result with the value of the coefficient of determination you obtained in the corresponding exercise in Section 4.3.

The square of $r$is

$(-0.9679{)}^2=0.9368$