5 Correlation And Regression
MATH 231: Basic Statistics
Homework #5 – Correlation and Regression:
1). Bi-lo Appliance Super-Store has outlets in several large metropolitan areas in New
England. The general sales manager aired a commercial for a digital camera on selected local TV stations prior ro a sale starting on Saturday and ending on Sunday. She obtained the information for Saturday-Sunday digital camera sales at the various outlets and paired it with the number of times the advertisement was shown on local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales. The data is below:
Location # of advertisement airings Sat-Sun Sales ($000)
Providence
4
15
Springfield
2
8
New Haven
5
21
Boston
6
24
Hartford
3
17
a). What is the dependent variable?
b). Draw a scatter diagram (draw, do not use Excel).
1 of 8
MATH 231: Basic Statistics
c). What is the correlation coefficient?
d). Interpret what the correlation coefficient means for this sample.
2 of 8
MATH 231: Basic Statistics
2). The following sample observations were randomly selected. x 4 5 3 6 10 y 4 6 5 7 7
a). What is the regression equation?
b). What is the expected value of y when x is 7?
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MATH 231: Basic Statistics
3). The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
Car Age (years) Selling Price ($000)
1
9
8.1
2
7
6.0
3
11
3.6
4
12
4.0
5
8
5.0
6
7
10.0
7
8
7.6
8
11
8.0
9
10
8.0
10
12
6.0
11
6
8.6
12
6
8.0
a). Draw a scatter diagram (draw, do not use Excel).
b). What is the correlation coefficient?
4 of 8
MATH 231: Basic Statistics
c). What is the regression equation?
d). Estimate the selling price of a 10-year old car.
e). Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative?
f). Interpret the
Homework #5 – Correlation and Regression:
1). Bi-lo Appliance Super-Store has outlets in several large metropolitan areas in New
England. The general sales manager aired a commercial for a digital camera on selected local TV stations prior ro a sale starting on Saturday and ending on Sunday. She obtained the information for Saturday-Sunday digital camera sales at the various outlets and paired it with the number of times the advertisement was shown on local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales. The data is below:
Location # of advertisement airings Sat-Sun Sales ($000)
Providence
4
15
Springfield
2
8
New Haven
5
21
Boston
6
24
Hartford
3
17
a). What is the dependent variable?
b). Draw a scatter diagram (draw, do not use Excel).
1 of 8
MATH 231: Basic Statistics
c). What is the correlation coefficient?
d). Interpret what the correlation coefficient means for this sample.
2 of 8
MATH 231: Basic Statistics
2). The following sample observations were randomly selected. x 4 5 3 6 10 y 4 6 5 7 7
a). What is the regression equation?
b). What is the expected value of y when x is 7?
3 of 8
MATH 231: Basic Statistics
3). The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
Car Age (years) Selling Price ($000)
1
9
8.1
2
7
6.0
3
11
3.6
4
12
4.0
5
8
5.0
6
7
10.0
7
8
7.6
8
11
8.0
9
10
8.0
10
12
6.0
11
6
8.6
12
6
8.0
a). Draw a scatter diagram (draw, do not use Excel).
b). What is the correlation coefficient?
4 of 8
MATH 231: Basic Statistics
c). What is the regression equation?
d). Estimate the selling price of a 10-year old car.
e). Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative?
f). Interpret the