Chapter 4: Q. 4.99 (page 182)

For Exercises 4.98 - 4.103,
(a) Compute SST, SSR, SSE using formula 4.2 on page 179.
(b) Compute the coefficient of determination, $r^{2}$ .
(c) Determine the percentage of variation in the observed values of the response variable explained by the regression and interpret your answer.
(d) State how useful the regression equation appears to be for making predictions.
Following are the age and price data for Corvettes from Exercise 4.59

Short Answer

Expert verified

(a) The values are $S S T = 25681.6; S S R = 24057.9; S S E = 1623.7$

(b) The coefiicient of variation is $0.9368$ .

(d) The regression line appears to be extremely useful, becausse there is less portion of unexplained variation present in the given data.

Step by step solution

Part (a) Step 1. Given Information.

A table of values.

Part (a) Step 2. Construct the table.

Construct the table.

Part (a) Step 3. Compute SST, SSR, SSE.

Find SST, SSR, SSE.

$S S T = \sum_{} y_{i}^{2} - \frac{{(\sum_{} y_{i})}^{2}}{2} = 1196690 - \frac{{(3422)}^{2}}{10} = 25681.6$

$S S R = \frac{[\sum_{} x_{i} y_{i} - {(\frac{\sum_{} x_{i} \sum_{} y_{i}}{n})}^{2}}{\sum_{} {x_{i}}^{2} - \frac{{(\sum_{} x_{i})}^{2}}{n}} = \frac{{[13168 - \frac{41 (3422)}{10}]}^{2}}{199 - \frac{41^{2}}{10}} = 24057.9 S S E = S S T - S S R = 25681.6 - 24057.9 = 1623.7$

Part (b) Step 1. FInd the coefficient of determination.

$r^{2} = \frac{S S R}{S S T} = \frac{24057.9}{25681.9} = 0.9368$

Part (c) Step 1. Find the percentage of variation.

The percentage of variatioon is $93.7 %$ .

It means that93.7%variation in price data is explained by age.

Part (d) Step 1. Useful for making predictions.

The regression line appears to be extremely useful, becausse there is less portion of unexplained variation present in the given data.

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Short Answer

Step by step solution

Part (a) Step 1. Given Information.

Part (a) Step 2. Construct the table.

Part (a) Step 3. Compute SST, SSR, SSE.

Part (b) Step 1. FInd the coefficient of determination.

Part (c) Step 1. Find the percentage of variation.

Part (d) Step 1. Useful for making predictions.

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