Practices
Exercise 2: The operations manager of a musical instrument distributor feels that demand for bass drums may be related to the number of television appearances by the popular rock group Green Shades during the preceding month. The manager has collected the data shown in the following table to make a plan on the recruiting numbers of sale representative with the demands of brass drums.
Demands for brass drum
Green Shades TV Appearances
3
3
6
4
7
7
5
6
10
8
8
5
(a) Using the equations presented in this chapter, compute the SST, SSE, and SSR. Find the least squares regression line for these data.
(b) What is your estimate for bass drum sales if the Green Shades performed on TV six times last month?
Exercise 3: Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follows:
Student
1
2
3
4
5
6
7
8
9
1st test grade
98
77
88
80
96
61
66
95
69
Final Average
93
78
84
73
84
64
64
95
76
(a) Develop a regression model that could be used to predict the final average in the course based on the first test grade.
(b) Predict the final average of a student who made an 83 on the first test.
(c) Give the values of r and for this model. Interpret the value of in the context of this problem.
Exercise 4: Steve Caples, a real estate appraiser in Lake Charles, Louisiana, has developed a regression model to help appraise residential housing in the Lake Charles area. The model was developed using recently sold homes in a particular neighborhood. The price (Y) of the house is based on the square footage (X) of the house. The model is The coefficient of correlation for the model is 0.63.
(a) Use the model to predict the selling price of a house that is 1,860 square feet.
(b) A house with 1,860 square feet recently sold for $95,000. Explain why this is not
Demands for brass drum
Green Shades TV Appearances
3
3
6
4
7
7
5
6
10
8
8
5
(a) Using the equations presented in this chapter, compute the SST, SSE, and SSR. Find the least squares regression line for these data.
(b) What is your estimate for bass drum sales if the Green Shades performed on TV six times last month?
Exercise 3: Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follows:
Student
1
2
3
4
5
6
7
8
9
1st test grade
98
77
88
80
96
61
66
95
69
Final Average
93
78
84
73
84
64
64
95
76
(a) Develop a regression model that could be used to predict the final average in the course based on the first test grade.
(b) Predict the final average of a student who made an 83 on the first test.
(c) Give the values of r and for this model. Interpret the value of in the context of this problem.
Exercise 4: Steve Caples, a real estate appraiser in Lake Charles, Louisiana, has developed a regression model to help appraise residential housing in the Lake Charles area. The model was developed using recently sold homes in a particular neighborhood. The price (Y) of the house is based on the square footage (X) of the house. The model is The coefficient of correlation for the model is 0.63.
(a) Use the model to predict the selling price of a house that is 1,860 square feet.
(b) A house with 1,860 square feet recently sold for $95,000. Explain why this is not