n Exercises 14.88-14.97, we repeat the data and provide the regres- sion equatio

Question

n Exercises 14.88-14.97, we repeat the data and provide the regres- sion equations for Exercises 14.48-14.57. In each exercise a. compute the three sums of squares, SST, SSR, and SSE, using the 14.96 defining formulas (Definition 14.6 on page 639). b. verify the regression identity, SST = SSR + SSE. c. compute the coefficient of determination d. determine the percentage of yariation in the observed values of 14.9 the response variable that is explained by the regression e. state how useful the regression equation appears to be for making predictions.

Explanation / Answer

From the given data

We calculate the predict and sum of square values by using the given regression equation

SSE = 6 , SST = 46 and SSR = 40

b) Clearly, SSE + SSR = 40+6 = 46 = SST

c) Coefficeint of determination r^2 = SSR / SST = 40/46= 0.86956

d) The 86.96 % variation in the observed values of the presponse variable variable that is explained

e) The predict regression equation is y = 1+2x, substitiute x values in x variable we get the Y values, and these are predict values

X Y X^2 Y^2 XY 0 1 0 1 0 4 9 16 81 36 3 8 9 64 24 1 4 1 16 4 2 3 4 9 6 Total: 10 25 30 171 70

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