Simple Linear Regression Model
Simple Linear Regression Model
1. The following data represent the number of flash drives sold per day at a local computer shop and their prices. | Price (x) | Units Sold (y) | | $34 | 3 | | 36 | 4 | | 32 | 6 | | 35 | 5 | | 30 | 9 | | 38 | 2 | | 40 | 1 |
| a. Develop as scatter diagram for these data. b. What does the scatter diagram indicate about the relationship between the two variables? c. Develop the estimated regression equation and explain what the slope of the line indicates. d. Compute the coefficient of determination and comment on the strength of relationship between x and y. e. Compute the sample correlation coefficient between the price and the number of flash drives sold. f. Perform a t test and determine if the price and the number of flash drives sold are related. Let α = 0.01. g. Perform an F test and determine if the price and the number of flash drives sold are related. Let α = 0.01. |
ANS:
b. Negative linear relationship. c. | = 29.7857 - 0.7286xThe slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units. | d. | r 2 = .8556; 85.56% of the variability in y is explained by the linear relationship between x and y. | e. | rxy = -0.92; negative strong relationship. | f. t = -5.44 < -4.032 (df = 5); reject Ho, and conclude x and y are related. g. | F = 29.642 > 16.26; reject Ho, x and y are related. |
2. Assume you have noted the following prices for books and the number of pages that each book contains.
| Book | Pages (x) | Price (y) | | A | 500 | $7.00 | | B | 700 | 7.50 | | C | 750 | 9.00 | | D | 590 | 6.50 | | E | 540 | 7.50 | | F | 650 | 7.00 | | G | 480 | 4.50 |
| a. Develop as scatter diagram for these data. b. What does the scatter diagram indicate about the relationship between the two variables? c. Develop the estimated regression equation and explain what the slope of the line indicates.
1. The following data represent the number of flash drives sold per day at a local computer shop and their prices. | Price (x) | Units Sold (y) | | $34 | 3 | | 36 | 4 | | 32 | 6 | | 35 | 5 | | 30 | 9 | | 38 | 2 | | 40 | 1 |
| a. Develop as scatter diagram for these data. b. What does the scatter diagram indicate about the relationship between the two variables? c. Develop the estimated regression equation and explain what the slope of the line indicates. d. Compute the coefficient of determination and comment on the strength of relationship between x and y. e. Compute the sample correlation coefficient between the price and the number of flash drives sold. f. Perform a t test and determine if the price and the number of flash drives sold are related. Let α = 0.01. g. Perform an F test and determine if the price and the number of flash drives sold are related. Let α = 0.01. |
ANS:
b. Negative linear relationship. c. | = 29.7857 - 0.7286xThe slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units. | d. | r 2 = .8556; 85.56% of the variability in y is explained by the linear relationship between x and y. | e. | rxy = -0.92; negative strong relationship. | f. t = -5.44 < -4.032 (df = 5); reject Ho, and conclude x and y are related. g. | F = 29.642 > 16.26; reject Ho, x and y are related. |
2. Assume you have noted the following prices for books and the number of pages that each book contains.
| Book | Pages (x) | Price (y) | | A | 500 | $7.00 | | B | 700 | 7.50 | | C | 750 | 9.00 | | D | 590 | 6.50 | | E | 540 | 7.50 | | F | 650 | 7.00 | | G | 480 | 4.50 |
| a. Develop as scatter diagram for these data. b. What does the scatter diagram indicate about the relationship between the two variables? c. Develop the estimated regression equation and explain what the slope of the line indicates.