Compute SSR, SSE, s Subscript e Superscript 2 , and the coefficient of determina

Question

Compute SSR, SSE, s Subscript e Superscript 2 , and the coefficient of determination, given the following statistics computed from a random sample of pairs of X and Y observations. Complete parts (a) through (e).

r Subscript xy Superscript 2 Baseline equals 0.50 nbsp

nequals

55

SSR

equals

(Type an integer or a decimal.)

SSE

equals

(Type an integer or a decimal.)

s Subscript e Superscript 2

equals

(Round to three decimal places as needed.)

Upper R squared

equals

(Type an integer or a decimal.)

b. Summation from i equals 1 to n left parenthesis y Subscript i Baseline minus y overbar right parenthesis squared equals 80 comma 000 nbsp

r Subscript xy Superscript 2 Baseline equals 0.60 nbsp

nequals

55

SSR

equals

(Type an integer or a decimal.)

SSE

equals

(Type an integer or a decimal.)

s Subscript e Superscript 2

equals

(Round to three decimal places as needed.)

Upper R squared

equals

(Type an integer or a decimal.)

c. Summation from i equals 1 to n left parenthesis y Subscript i Baseline minus y overbar right parenthesis squared equals 270 nbsp

r Subscript xy Superscript 2 Baseline equals 0.90 nbsp

nequals

55

SSR

equals

(Type an integer or a decimal.)

SSE

equals

(Type an integer or a decimal.)

s Subscript e Superscript 2

equals

(Round to three decimal places as needed.)

Upper R squared

equals

(Type an integer or a decimal.)

d. Summation from i equals 1 to n left parenthesis y Subscript i Baseline minus y overbar right parenthesis squared equals 220 comma 000 nbsp

r Subscript xy Superscript 2 Baseline equals 0.20 nbsp

nequals

68

SSR

equals

(Type an integer or a decimal.)

SSE

equals

(Type an integer or a decimal.)

s Subscript e Superscript 2

equals

nothing

(Round to three decimal places as needed.)

Upper R squared

equals

(Type an integer or a decimal.)

e. Summation from i equals 1 to n left parenthesis y Subscript i Baseline minus y overbar right parenthesis squared equals 20 comma 000 nbsp

r Subscript xy Superscript 2 Baseline equals 0.40 nbsp

nequals

40

SSR

equals

(Type an integer or a decimal.)

SSE

equals

(Type an integer or a decimal.)

s Subscript e Superscript 2

equals

nothing

(Round to three decimal places as needed.)

Upper R squared

equals

(Type an integer or a decimal.)

r Subscript xy Superscript 2 Baseline equals 0.50 nbsp

Explanation / Answer

   Formula used

coefficient of determination = R^2

SST = Sum ( y_i - y bar)^2

SSR = R^2 * SST    

SSE = SST(1 - R^2)

s^2 = SSE/(n-2)

a) You have not provided SST (Sum ( y_i - y bar)^2)

b) here r^2 = 0.60

SST = 80,000

n = 55

hence coefficient of determination = 0.60

SSR = 80000*0.60 = 48000

SSE = SST - SSR = 32000

s^2 = SSE/(n-2) = 32000/53 = 603.77358

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