MS Mod 16 Regression summary statistics practice exam questions


MS Mod 16 Regression summary statistics practice exam questions

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MS Module 16 Regression summary statistics practice exam questions

(The attached PDF file has better formatting.)

A regression analysis on 11 data points has summary statistics

●    xi = 8
●    yi = 15
●    xi2 = 41
●    yi2 = 55
●    xiyi = 41


Question 16.1:

What is , the average X value?

Answer 16.1: 8 / 11 = 0.727273

(average = total / number of observations)



Question 16.2:

What is , the average Y value?

Answer 16.2: 15 / 11 = 1.363636

(average = total / number of observations)



Question 16.3: Sxx

What is Sxx, the sum of squares of the X values?

Answer 16.3: 41 – 0.7272732 × 11 = 35.182

(Sxx, the sum of squared deviations of the X values, is xi2 – N × 2)



Question 16.4: Syy

What is Syy, the sum of squares of the Y values?

Answer 16.4: 55 – 1.3636362 × 11 = 34.545

(Syy, the sum of squares of the Y values, is yi2 – N × 2)


Question 16.5: Sxy

What is Sxy, the cross sum of squares of the X and Y values?

Answer 16.5: 41 – 8 × 15 / 11 = 30.091

(Sxy, the cross sum of squares of the X and Y values, is xiyi – N × × = xiyi – xi × yi / N)



Question 16.6: Least squares estimate for β1

What is the least squares estimate for β1?

Answer 16.6: 30.091 / 35.182 = 0.855

(least squares estimate for β1 = Sxy / Sxx)


Question 16.7: Least squares estimate for β0

What is the least squares estimate for β0?

Answer 16.7: 1.364 – 0.727 × 0.855 = 0.742

(least squares estimate for β0 = – × β1)



Question 16.8: Error sum of squares

What is the error sum of squares?

Answer 16.8: 55 – 0.742 × 15 – 0.855 × 41 = 8.815; with more significant digits for β0 and β1, ESS = 8.809

(error sum of squares SSE is yi2 – β0 × yi – β1 × xiyi)


Question 16.9: Least squares estimate for σ2

What is s2, the least squares estimate for σ2?

Answer 16.9: 8.809 / (11 – 2) = 0.979

(least squares estimate for σ2 = error sum of squares / (number of observations – 2) )


Question 16.10: Least squares estimate for σ

What is s, the least squares estimate for σ?

Answer 16.10: 0.9790.5 = 0.989

(standard deviation = square root of variance)



Question 16.11: Standard deviation of least squares estimate for β1

What is the standard deviation of the least squares estimate for β1?

Answer 16.11: 0.989 / 35.1820.5 = 0.167

(the standard deviation of the least squares estimate for β1 = σ / Sxx0.5)


Question 16.12: R2

What is the least squares estimate for R2?

Answer 16.12: 1 – 8.809 / 34.545 = 0.745

(the least squares estimate for R2 = 1 – error sum of squares / Syy)


Question 16.13: Correlation

What is the estimated correlation ρ between X and Y?

Answer 16.13: 30.091 / (35.182 × 34.545)0.5 = 0.863

(the estimated correlation ρ between X and Y = Sxy / (Sxx × Syy)0.5



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