Lecture 11 - Practice Questions PDF

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Ryerson University W21 QMS 202 Practice Questions for Lecture 11 Dr Boˇza Tasi´c 1. In the straight line portion Yi = β0 +β1 Xi of the simple linear regression model Yi = β0 + β1 Xi + ǫi , the Y intercept β0 represents the a) predicted value of Y. b) variation around the sample regression line. c) change in estimated Y per unit change in X. d) predicted value of Y when X = 0. 2. In the straight line portion Yi = β0 +β1 Xi of the simple linear regression model Yi = β0 + β1 Xi + ǫi , the slope β1 represents the a) predicted value of Y when X = 0. b) the estimated average change in Y per unit change in X. c) the predicted value of Y. d) variation around the line of regression. Use the following scenario for problems 3-6 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below. City Price ($) River Falls 1.30 Hudson 1.60 Ellsworth 1.80 Prescott 2.00 Rock Elm 2.40 Stillwater 2.90

Sales 100 90 90 40 38 32

2 3. The estimated regression line for forecasting the sales (Y) based on the price (X) is a) Yˆ = 3.112X + 19.996 b) Yˆ = −48.193X + 161.386 c) Yˆ = −4.193X + 16.386 d) Yˆ = 48.193X − 161.386 4. If the price of the candy bar is set at $2.2, the predicted sales will be? ( Round your answer to the nearest integer) Answer: 5. What is the estimated mean change in the sales of the candy bar if price goes up by $1.00? a) 161.386 b) 0.784 c) -48.193 d) -3.810 6. Which of the following statements is not true? a) As the price of the candy bar goes up the sales will decrease. b) If the price of candy goes up by $2 the sales will drop by $96.4 c) If the price of candy goes down by $1 the sales will go up by $48.2 d) If the price of the candy bar goes down the sales will decrease.

3 Use the following scenario for problems 7-11 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses six small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below. City Price ($) River Falls 1.30 Hudson 1.60 Ellsworth 1.80 Prescott 2.00 Rock Elm 2.40 Stillwater 2.90

Sales 100 90 90 40 38 32

7. What is the standard error of the regression slope estimate, Sb1 , for the data? a) 0.784 b) 0.885 c) 12.650 d) 16.299 8. What alternative hypothesis H1 would you use to test if there is a significant relationship between the sales and price for the data? a) H1 : There is no linear relationship b) H1 : The slope is zero c) H1 : β1 6= 0 d) H1 : ρ 6= 0 e) Either c) or d)

4 9. To test that the regression coefficient, β1 , is not equal to 0, what would be the t critical values? Use α = 0.05. a) ±2.5706 b) ±2.7764 c) ±3.1634 d) ±3.4954 e) None of the above 10. A 95% confidence interval estimate of the population slope β1 is a) [26.3 , 96.5] b) [116.5 , 196.9] c) [-106.3 , -86.5] d) [-83.3 , -13.1] e) None of the above 11. Which of the following statements are correct? I) The correlation coefficient between the price and sales is r = 0.8854. II) The test statistic you would use to test the hypothesis that the price did not affect the amount of sales generated is tST AT = −3.8097 III) The p-value you would use to test the hypothesis that there is no correlation between the prices and sales is p = 0.0189 IV) At α = 0.05 we conclude that there is a linear relationship between the price and the amount of sales. a) I and II b) I, II and III c) I, II and IV d) II, III and IV e) All of the statements are correct

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Answers 1. d) 2. b) 3. b) 4. 55 5. c) 6. d) 7. c) 8. e) 9. b) 10. d) 11. d)

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