Question
In: Statistics and Probability
A local shop owner would like to know if he can predict weekly sales by knowing...
A local shop owner would like to know if he can predict weekly sales by knowing the number of customers who visit his shop in the week. He takes a random sample of 10 weeks from the previous year, recording the number of customers and the sales in thousands of dollars. The results are summarized in the table below. He has assumed that the sales are normally distributed.
| week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| customers | 794 | 799 | 837 | 855 | 845 | 844 | 863 | 875 | 880 | 841 |
| sales($000) | 9.33 | 8.26 | 7.48 | 9.08 | 9.83 | 10.09 | 11.01 | 11.49 | 12.07 | 9.64 |
a. Find the equation for the regression line.
b. Interpret the slope in terms of this problem.
c. Interpret the y-intercept for this problem.
d. Interpret the coefficient of determination in terms of this problem.
e. Find the correlation coefficient.
f. If 800 customers visited his shop in one week, what would he predict as his sales for that week?
g. If 700 customers visited his shop in one week, what would he predict as his sales for that week?
h. Do the data indicate a strong linear relationship between the number of customers and sales at the 5% significance level?
Solutions
orchestra answered 1 year agoRelated Solutions
The owner of a movie theater company would like to predict weekly gross revenue as a...
The owner of a movie theater company would like to predict
weekly gross revenue as a function of advertising expenditures.
Historical data for a sample of eight weeks follow.
Weekly
Gross
Revenue
($1,000s)
Television
Advertising
($1,000s)
Newspaper
Advertising
($1,000s)
96
5
1.5
90
2
2
95
4
1.5
93
2.5
2.5
95
3
3.3
94
3.5
2.2
94
2.5
4.1
94
3
2.5
(a)
Use α = 0.01 to test the hypotheses
H0:
β1 = β2 = 0
Ha:
β1...
The owner of a movie theater company would like to predict weekly gross revenue as a...
The owner of a movie theater company would like to predict
weekly gross revenue as a function of advertising expenditures.
Historical data for a sample of eight weeks follow.
Weekly
Gross
Revenue
($1,000s)
Television
Advertising
($1,000s)
Newspaper
Advertising
($1,000s)
96
5
1.5
91
2
2
95
4
1.5
93
2.5
2.5
95
3
3.3
94
3.5
2.3
94
2.5
4.1
94
3
2.5
(a)
Use α = 0.01 to test the hypotheses
H0:
β1 = β2 = 0
Ha:
β1...
The owner of a movie theater company would like to predict weekly gross revenue as a...
The owner of a movie theater company would like to predict
weekly gross revenue as a function of advertising expenditures.
Historical data for a sample of eight weeks follow.
Weekly
Gross
Revenue
($1,000s)
Television
Advertising
($1,000s)
Newspaper
Advertising
($1,000s)
96
5
1.5
90
2
2
95
4
1.5
93
2.5
2.5
95
3
3.3
94
3.5
2.3
94
2.5
4.1
94
3
2.5
1. Use α = 0.01 to test the hypotheses
H0:
β1 = β2 = 0
Ha:
β1...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., would like to
predict weekly gross revenue as a function of advertising
expenditures. Historical data for a sample of eight weeks follow
has been collected in the Microsoft Excel Online file below. Open
the spreadsheet and perform the required analysis to answer the
questions below.
Weekly Gross Revenue ($1000s)
Television Advertising ($1000s)
Newspaper Advertising($1000s)
97
6
1.5
91
2
2
96
5
1.5
93
2.5
2.5
95
4
3.3
94
3.5
2.3
95...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., would like to
predict weekly gross revenue as a function of advertising
expenditures. Historical data for a sample of eight weeks follow.
Weekly Gross Revenue ($1000s) Televison Advertising ($1000s)
Newspaper Advertising ($1000s) 97 5 1.5 90 2 3 96 4 2.5 92 2.5 2.5
95 3 3.3 95 3.5 2.3 95 2.5 4.2 95 3 3.5 Use = .01 to test the
hypotheses for the model y = 0 + 1 x 1...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., would like to
predict weekly gross revenue as a function of advertising
expenditures. Historical data for a sample of eight weeks
follow.
Weekly Gross Revenue ($1000s)
Televison Advertising ($1000s)
Newspaper Advertising ($1000s)
97
5
1.5
90
2
3
96
4
2.5
93
3.5
2.5
96
3
4.3
94
3.5
2.3
95
2.5
5.2
95
3
3.5
a. Use to test the hypotheses
and/or is not equal to zero
for the model , where
television advertising...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., would like to
predict weekly gross revenue as a function of advertising
expenditures. Historical data for a sample of eight weeks
follow.
Weekly
Gross
Revenue
($1,000s)
Television
Advertising
($1,000s)
Newspaper
Advertising
($1,000s)
96
5.0
1.5
90
2.0
2.0
95
4.0
1.5
92
2.5
2.5
95
3.0
3.3
94
3.5
2.3
94
2.5
4.2
94
3.0
2.5
(a)
Develop an estimated regression equation with the amount of
television advertising as the independent variable. (Round...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a...
The owner of Showtime Movie Theaters, Inc., would like to
predict weekly gross revenue as a function of advertising
expenditures. Historical data for a sample of eight weeks
follow.
Weekly
Gross
Revenue
($1,000s)
Television
Advertising
($1,000s)
Newspaper
Advertising
($1,000s)
96
5.0
1.5
90
2.0
2.0
95
4.0
1.5
92
2.5
2.5
95
3.0
3.3
94
3.5
2.3
94
2.5
4.2
94
3.0
2.5
(a)
Develop an estimated regression equation with the amount of
television advertising as the independent variable. (Round...
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