# Question: As we noted because of the regression identity we can

As we noted, because of the regression identity, we can express the coefficient of determination in terms of the total sum of squares and the error sum of squares as r2 = 1 − SSE/SST.

a. Explain why this formula shows that the coefficient of determination can also be interpreted as the percentage reduction obtained in the total squared error by using the regression equation instead of the mean, y-bar, to predict the observed values of the response variable.

b. Refer to Exercise 4.89. What percentage reduction is obtained in the total squared error by using the regression equation instead of the mean of the observed prices to predict the observed prices?

a. Explain why this formula shows that the coefficient of determination can also be interpreted as the percentage reduction obtained in the total squared error by using the regression equation instead of the mean, y-bar, to predict the observed values of the response variable.

b. Refer to Exercise 4.89. What percentage reduction is obtained in the total squared error by using the regression equation instead of the mean of the observed prices to predict the observed prices?

## Answer to relevant Questions

y = 32 + 1.8x (from Exercise 4.7) a. Find the y-intercept and slope of the specified linear equation. b. Explain what the y-intercept and slope represent in terms of the graph of the equation. c. Explain what the y-intercept ...a. Definition 4.7 on page 171. b. Formula 4.3 on page 171. Compare your answers in parts (a) and (b). Following are the size and price data for custom homes from Exercises 4.52 and 4.90. a. Obtain the linear correlation coefficient. b. Interpret the value of r in terms of the linear relationship between the two variables in ...The data from Exercise 4.64 for number of birdies during a tournament and final score for 63 women golfers are on the WeissStats CD. In exercise How important are birdies (a score of one under par on a given golf hole) in ...In the article "Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy" (American Industrial Hygiene Association Journal, Vol. 63, pp. 756-761), I. Moa et al. reported on determining fiber ...Post your question