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Chapter 4: Q. 4.95 (page 181)

We repeat the data and provide the regression equations.

Part (a): Compute the three sums of squares, SST, SSR and SSE using the defining formulas.

Part (b): Verify the regression identity,SST=SSR+SSE.

Part (c): Compute the coefficient of determination.

Part (d): Determine the percentage of variation in the observed values of the response variable that is explained by the regression.

Part (e): State how useful the regression equation appears to be for making predictions.

Short Answer

Expert verified

Part (a): The three sums of squares, SST, SSR and SSE are 14,8and 6respectively.

Part (b): Substitute the values of SSR and SSE in the formula of SST, to verify the given regression identity.

Part (c): The coefficient of determination is 0.571.

Part (d): The percentage of variation in the observed values of the response variable that is explained by the regression is 57.1%.

Part (e): The regression is moderately useful for making predictions.

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given question,

02

Part (a) Step 2. Write the formulas of three sums of squares, SST, SSR and SSE.

We know,

SST=危yi-y2,SSR=危y铃�i-y2,SSE=危yi-y铃�i2

On constructing the table,

From the table,

SST=14,SSR=8,SSE=6

03

Part (b) Step 1. Verify the equation of SST.

In regression, the equation,

SST=SSR+SSE14=8+614=14

Thus, the regression identity is verified.

04

Part (c) Step 1. Compute the coefficient of determination.

Consider the coefficient of determination,

r2=1-SSRSST=1-614=1-0.429=0.571

05

Part (d) Step 1. Determine the percentage of variation.

As the coefficient of determination is 0.571.

Then we can say that 57.1%of the variation in the observed value is explained by the regression.

06

Part (e) Step 1. State usefulness of the regression equation.

On stating the usefulness of the regression equation,

We can say that here the regression is moderately useful for making predictions as the coefficient of determination is 57.1%. That is, the coefficient of determination is more than 50%.

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Most popular questions from this chapter

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