Question
In: Statistics and Probability
A chain store corporation wants study the effects of price decrease (x1, in %) and advertising expenditure increase (x2) on sales volume (y).
A chain store corporation wants study the effects of price decrease (x1, in %) and advertising expenditure increase (x2) on sales volume (y). The corporation imposes different levels of price decrease and advertising expenditure increase on its product in stores in eight different districts of the country and measures the changes in sales volume over the next three months. A multiple regression model is used and the following output is extracted from the computer software.
ANOVA
| df | SS | MS | F | |
| Regression | ? | ? | ? | ? |
| Residual | ? | ? | ? | |
| Total | ? | ? |
| Coefficients | Standard Error | |||
| Intercept | 0.1285 | 0.9018 | ||
| x1 | 0.0471 | 0.1213 | ||
| x2 | 0.4141 | 0.1742 | ||
i. Write down the fitted multiple linear regression equation. [1 mark]
ii. Complete the above ANOVA table for the multiple linear regr P ession if y = 42, Py 2 = 256 and only 7.66% of variation in sales volume cannot be explained by price decrease and advertising expenditure. [3 marks]
iii. Test the overall significance of the fitted equation in part i. at 1% level of significance. [3 marks]
iv. Test the significance of price decrease in affecting the sales volume at 1% level of significance
Solutions
orchestra answered 1 year agoRelated Solutions
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?1x1 = advertising expenditure
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In a study relating consumption expenditure (Y) on income (X2) and wealth (X3) based on 10...
In a study relating consumption expenditure (Y) on income (X2)
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was obtained
Yhat = 24.337 + 0.08764X2 - 0.0349X3
SE
(6.2801) (0.31438) (0.0301)
t
(3.875)
(2.7726)
(-1.1595)
i) In your opinion, what type of problem takes in this result?
Explain it
ii) What are the practical consequences of this
problem?
iii) What are the theoretical of this problem
iv) How to detect this problem?
v)In your judgement,...
A regression analysis relating a company’s sales, their advertising expenditure, price, and time resulted in the...
A regression analysis relating a company’s sales, their
advertising expenditure, price, and time resulted in the
following.
Regression Statistics
Multiple R
0.8800
R Square
0.7744
Adjusted R Square
0.7560
Standard Error
232.29
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
3
53184931.86
17728310.62
328.56
0.0000
Residual
21
1133108.30
53957.54
Total
24
54318040.16
Coefficients
Standard Error
t Stat
P-value
Intercept
927.23
1229.86
0.75
0.4593
Advertising (X1)
1.02
3.09
0.33
0.7450
Price (X2)
15.61
5.62
2.78
0.0112
Time (X3)
170.53...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and
its advertising expenditure over a period of 8 years.
Advertising (x)
Sales (y)
400,000
6,000,000
500,000
7,200,000
500,000
8,000,000
660,000
7,500,000
790,000
8,900.000
540,000
8,100,000
420,000
5,900.000
380,000
4,000,000
If the company's advertising expenditure is $315,000, what are
the predicted sales?
If the company wanted $9,500,000 in sales, what should the
advertising budget be?
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and
its advertising expenditure over a period of 8 years.
Sales in
Millions of Dollars
Advertising
in ($10,000)
11
32
16
33
18
35
17
34
16
36
19
37
19
39
24
42
a.
Which variable is the dependent variable?
b.
Using the Excel spreadsheet, run the least squares model and
write the summary output here.
c.
If the company's advertising expenditure is $400,000, what are
the predicted sales? Give...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and
its advertising expenditure over a period of 8 years.
(Y)
Sales in
Millions of Dollars
(X)
Advertising
in ($10,000)
14
32
15
33
18
35
17
34
16
36
a.
Develop a scatter diagram of sales versus advertising and
explain what it shows regarding the relationship between sales and
advertising.
b.
Use the method of least squares to compute an estimated
regression line between sales and advertising.
c.
If the...
The following data represent a company’s yearly sales volume and its advertising expenditure over a period...
The following data represent a company’s yearly sales
volume and its advertising expenditure over a period of 8
years.
Year
Sales
(Y)
Advertising (X)
1989
15
32
1990
16
33
1991
18
35
1992
17
34
1993
16
36
1994
19
37
1995
19
39
1996
24
42
Develop a scatter diagram of sales versus
advertising
Use the method of least squares to compute an estimated
regression line between sales and advertising.
If the company’s advertising expenditure is $40, what...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and
its advertising expenditure over a period of 8 years.
(Y)
(X)
Sales in
millions
Advertising in ($10,000)
15
32
16
33
18
35
17
34
16
36
(a) Develop a scatter diagram of sales versus advertising and
explain what it shows regarding the relationship between sales and
advertising.
(b) Use the method of least squares to compute an estimated
regression line between sales and...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a
company's yearly sales volume and its advertising expenditure over
a period of 8 years.
Sales (Millions)
Advertising ($10,000)
15
32
16
33
18
35
17
34
16
36
19
37
19
39
24
42
To make sure the Excel regression package is
installed.
Click “Tools”,
à“Add-Ins”
àchoose “Analysis Toolpak” and click
“OK”.
To use the Excel regression
package,
Click “Tools”, à“Data
Analysis” and click “Regression”.
a. Use
the method of least squares to compute...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and
its advertising expenditure over a period of 5 years. (Y) Sales in
Millions of Dollars 15 16 18 17 16 (X) Advertising in ($10,000) 32
33 35 34 36
(a) Compute the coefficient of determination for the estimated
regression equation you got in the previous in-class problem.
(b) Interpret the meaning of the value of the coefficient of
determination that you found in (a). Be very specific.
(c) Perform a...
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