Question
In: Math
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 Advertising (X) Millions of Dollars 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 advertising by computing b0 and b1.
(c) If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.
(d) What does the slope of the estimated regression line indicate?
Solutions
Expert Solution
a) Scatter plot using excel :
Select the data set (x,y) ---> Go to Insert menu --> Charts ---> Scatter
b) Equation of regression line : y = b0 + b1*x
Sums ∑x = 170 , ∑y = 82, ∑x*y = 2792, ∑x2 = 5790 and
∑y2 = 1350 , 
= 34 ,
= 16.4
Slope b1 = 
= 
Slope b1 = 0.4
Intercept b0 = -
b1* = 16.4 - (
0.4*34 )
Intercept b0 = 2.8
Equation of regression line : Sales (Y) = 2.8 + 0.4*advertisement (X)
c ) company's advertising expenditure is $400,000, We are given x = 40
Sales (Y) = 2.8 + 0.4*40
Sales (Y) = 18.8 or $188000
d) Interpretation of slope :
If there is increase in advertising expenditure by $1 then we expect to increase in company's yearly sales volume by $0.4
milcah answered 1 year agoRelated Solutions
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.
(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...
The following data represent a company's yearly sales and its advertising expenditure over a period of...
The following data represent a company's yearly sales and its
advertising expenditure over a period of 8 years.
Advertising Expenditure (in $10,000)
(x)
Sales in
Millions of Dollars (y)
32
15
33
16
34
18
34
17
35
16
37
18
39
21
40
24
a.
Develop a scatter diagram of sales versus advertising
and explain what it shows regarding the
relationship between sales and advertising.
b.
Compute an estimated regression equation between sales and
advertising.
c.
If the...
The following data represent a company's yearly sales and its advertising expenditure over a period of...
The following data represent a company's yearly sales and its
advertising expenditure over a period of 8 years.
Advertising Expenditure (in $10,000)
(x)
Sales in
Millions of Dollars (y)
32
15
33
16
34
18
34
17
35
16
37
18
39
21
40
24
a.
Develop a scatter diagram of sales versus advertising
and explain what it shows regarding the
relationship between sales and advertising.
b.
Compute an estimated regression equation between sales and
advertising.
c.
If the...
The following data represent a company's yearly sales and its advertising expenditure over a period of...
The following data represent a company's yearly sales and its
advertising expenditure over a period of 8 years.
Advertising Expenditure (in $10,000)
(x)
Sales in
Millions of Dollars (y)
32
15
33
16
34
18
34
17
35
16
37
18
39
21
40
24
a.
Develop a scatter diagram of sales versus advertising
and explain what it shows regarding the
relationship between sales and advertising.
b.
Compute an estimated regression equation between sales and
advertising.
c.
If the...
The following data represent a company's yearly sales and its advertising expenditure over a period of...
The following data represent a company's yearly sales and its
advertising expenditure over a period of 8 years.
Sales in Millions of Dollars (y)
Advertising Expenditure (in $10,000) (x)
15
32
16
33
18
35
17
34
16
36
19
37
19
39
24
42
a. Use the method of least squares to compute an estimated
regression equation between sales and advertising
b. If the company's advertising expenditure is $400,000,...
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