91Ó°ÊÓ

The given data is

The below table gives the prices of randomly selected $10$Corvettes with their age between 1 and 6 years inclusively. The age is denoted by $x$, and the price is denoted by $y$in hundreds of dollars.

The formulas to calculate the sum of squares is

$SST=∑y_i^2-{\left(∑y_i\right)}^2/n$

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

$SSE=SST-SSR$

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

$SST=1196690-\frac{{3422}^2}{10}$

localid="1653298850723" $=25681.6$

$$\begin{gathered} SSR=\frac{|13168-41×3422÷10{|}^2}{199-4{⌋}^2÷10} \\ SSR=24057.8913 \end{gathered}$$

$$\begin{gathered} SSE=25681.6-24057.8913 \\ SSE=1623.7087 \end{gathered}$$

The given data is

The coefficient of determination is

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

$$\begin{gathered} =\frac{24057.8913}{25681.6} \\ =0.9368 \end{gathered}$$

The given data is

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

$0.9368=93.68\%$

The given data is

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

The computed $r^2=0.9368$, which is extremely near to 1.

As a result, utilising the regression equation to create predictions is quite effective, and the regression can explain roughly 94% of the variation.