The owner of a restaurant in Bloomington, Indianna, has recorded sales data for the past 10 years. He has also recorded data on potentially relevant variables. The following table gives data on sales and other potentially relevant variables for that particular restaurant. Sales (thousands of dollars) Year Population Advertising (thousands of dollars) Previous advertising (thousands of dollars) $15713 1 102558 $20 $30 $12937 2 101792 $15 $20 $12872 3 104347 $25 $15 $16227 4 106180 $30 $25 $15388 5 106562 $15 $30
The owner of a restaurant in Bloomington, Indianna, has recorded sales data for the past 10 years. He has also recorded data on potentially relevant variables. The following table gives data on sales and other potentially relevant variables for that particular restaurant.
Sales (thousands of dollars) |
Year |
Population |
Advertising (thousands of dollars) |
Previous advertising (thousands of dollars) |
$15713 |
1 |
102558 |
$20 |
$30 |
$12937 |
2 |
101792 |
$15 |
$20 |
$12872 |
3 |
104347 |
$25 |
$15 |
$16227 |
4 |
106180 |
$30 |
$25 |
$15388 |
5 |
106562 |
$15 |
$30 |
$13180 |
6 |
105209 |
$25 |
$15 |
$17199 |
7 |
109185 |
$35 |
$25 |
$20674 |
8 |
109976 |
$40 |
$35 |
$20350 |
9 |
110659 |
$20 |
$40 |
$14444 |
10 |
111844 |
$25 |
$20 |
Consider the model: salest = 0 + 1t + 2popt + 3advt + 4advt-1 + t
where salest = sales in year t,
popt = size of the population residing within 10 kilometres of the restaurant,
advt = advertising expenditures in year t, and
advt-1 = advertising expenditures in the previous year.
Based on the sample data, a
SUMMARY OUTPUT |
||||||
Regression Statistics |
||||||
Multiple R |
0,994630788 |
|||||
R Square |
0,989290405 |
|||||
Adjusted R Square |
0,980722728 |
|||||
Standard Error |
393,1191142 |
|||||
Observations |
10 |
|||||
ANOVA |
||||||
|
df |
SS |
MS |
F |
Significance F |
|
Regression |
4 |
71378769,21 |
17844692,3 |
115,4677605 |
4,12255E-05 |
|
Residual |
5 |
772713,1899 |
154542,638 |
|||
Total |
9 |
72151482,4 |
|
|
|
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Intercept |
24799,62737 |
17008,82164 |
1,458045001 |
0,204627778 |
-18922,94058 |
68522,19531 |
Year |
318,9594603 |
178,6691756 |
1,785195791 |
0,134293268 |
-140,3242772 |
778,2431977 |
Population |
-0,20186378 |
0,172483261 |
-1,17033838 |
0,294606217 |
-0,645246117 |
0,241518557 |
Advertising |
134,947818 |
19,58889716 |
6,888995176 |
0,000986635 |
84,59295482 |
185,3026813 |
Previous_Advertising |
295,5352939 |
19,53921967 |
15,12523524 |
2,2891E-05 |
245,3081307 |
345,762457 |
You are required to answer the following questions:
- Estimate the sample regression equation.
- What proportion of variation in annual sales is explained by variation in year, population size, advertising expenditure for current year and advertising expenditure for previous year?
- Construct a 99% confidence interval for From this confidence interval, can you conclude that previous year advertising expenditure influence current year sales?
- Test at 5% level of significance the hypothesis that year, population size, advertising expenditure for current year and advertising expenditure for previous year jointly influence annual sales.
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