91Ó°ÊÓ

The given data is

$\hat{y}=9-2x$

The given regression equation is

$\hat{y}=9-2x$

Formulas to calculate the sum of squares is

$$\begin{gathered} SST=∑{\left(y_i-\stackrel{¯}{y}\right)}^2 \\ SST=∑{\left({\hat{y}}_i-\stackrel{¯}{y}\right)}^2 \\ SST=∑{\left(y_i-\hat{y}\right)}^2 \end{gathered}$$

As shown in the table below, the relevant sums can be determined.

$$\begin{gathered} SST=38 \\ SSR=24 \\ SSE=14 \end{gathered}$$

The given data is

$\hat{y}=9-2x$

From the above answer

$SST=SSR+SSE$

$$\begin{gathered} =24+14 \\ =38 \end{gathered}$$

The given data is

$\hat{y}=9-2x$

The formula for the coefficient of determination is

$r^2=\frac{SSR}{SST}$

$$\begin{gathered} =\frac{24}{38} \\ =0.6316 \end{gathered}$$

The given data is

$\hat{y}=9-2x$

The coefficient of determination restated as a percentage is the percentage of variation:

$0.6316=63.16\%$

The given data is

$\hat{y}=9-2x$

The regression equation can be used to generate predictions if the estimated $r^2$is near to $1$.

The computed $r^2$is $0.6316$, which is a long way from $1$.

As a result, utilising the regression equation to generate predictions is not practical, and the regression can only explain around $63\%$ of the variation.