## MS Mod 16 Regression summary statistics practice exam questions

 Author Message NEAS Supreme Being         Group: Administrators Posts: 4.2K, Visits: 1.2K 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 = 41Question 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: SxxWhat 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: SyyWhat 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 β1What 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 β0What 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 squaresWhat 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 σ2What 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 σWhat 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 β1What 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: CorrelationWhat 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 Attachments MS Module 16 Regression summary statistics practice exam questions.pdf (219 views, 40.00 KB)
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