## MS Mod 17 Confidence interval and prediction interval practice exam...

 Author Message NEAS Supreme Being         Group: Administrators Posts: 4.2K, Visits: 1.2K MS Module 17 Confidence interval and prediction interval practice exam questions(The attached PDF file has better formatting.)A linear regression analysis relates Y to X. ●    The X values are {1, 2, …, 7}●    The least squares estimator for β1 is a linear function of the Y values =  ciYi●    The error sum of squares (SSE) is 25Question 17.2: What is , the average X value?Answer 17.2: (1 + 7) / 2 = 4Question 17.3: SxxWhat is Sxx, the sum of squared residuals for the X values?Answer 17.3: (1 – 4)2 + (2 – 4)2 + (3 – 4)2 + (4 – 4)2 + (5 – 4)2 + (6 – 4)2 + (7 – 4)2 = 28Question 17.4: Least squares estimate of σ2What is s2, the estimate of σ2?Answer 17.4: 25 / (7 – 2) = 5(least squares estimate of σ2 = SSE / (number of observations – 2) )Question 17.5: Least squares estimate of σWhat is s, the estimate of σ?Answer 17.5: 50.5 = 2.2361(standard deviation = square root of variance)Question 17.6: Standard deviation of the least squares estimate of β1What is the standard deviation of the least squares estimate of β1?Answer 17.6: 2.2361 / 280.5 = 0.4226(standard deviation = square root of variance)Question 17.7: t value for 90% two-sided confidence intervalWhat is the t value for a 90% two-sided confidence interval?Answer 17.7: 2.015(Table look-up)Question 17.8: Width of confidence intervalWhat is the width of the 90% confidence interval at x = 2?Answer 17.8: 2 × 2.2361 × 2.015 × (1 / 7 + (2 – 4)2 / 28)0.5 = 4.8168(width of the confidence interval is 2 × tα/2,n-2 × s × (1/n + (x* – )2 / Sxx )½ )Question 17.9: Width of prediction intervalWhat is the width of the 90% prediction interval at x = 2?Answer 17.9: 2 × 2.2361 × 2.015 × (1 + 1 / 7 + (2 – 4)2 / 28)0.5 = 10.2181(width of the confidence interval is 2 × tα/2,n-2 × s × (1 + 1/n + (x* – )2 / Sxx )½ ) Attachments MS Module 17 Confidence intervalprediction interval practice exam questions.pdf (240 views, 45.00 KB)
##### Merge Selected
Merge into selected topic...

Merge into merge target...

Merge into a specific topic ID...