# Question: Let the sample regression line be yi b0 b1xi

Let the sample regression line be

yi = b0 + b1xi + ei = y`i + ei (i = 1, 2, c, .., n)

and let x and y denote the sample means for the independent and dependent variables, respectively.

a. Show that

ei = yi – y-bar – b(xi – x-bar)

b. Using the result in part a, show that

c. Using the result in part a, show that

d. Show that

y`i – y-bar = bi(xi – x-bar)

e. Using the results in parts c and d, show that

SST = SSR + SSE

yi = b0 + b1xi + ei = y`i + ei (i = 1, 2, c, .., n)

and let x and y denote the sample means for the independent and dependent variables, respectively.

a. Show that

ei = yi – y-bar – b(xi – x-bar)

b. Using the result in part a, show that

c. Using the result in part a, show that

d. Show that

y`i – y-bar = bi(xi – x-bar)

e. Using the results in parts c and d, show that

SST = SSR + SSE

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