Question
In: Statistics and Probability
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?
Solutions
Expert Solution
| X | Y | XY | X^2 | Y^2 |
| 400,000 | 6,000,000 | 2.4E+12 | 1.6E+11 | 3.6E+13 |
| 500,000 | 7,200,000 | 3.6E+12 | 2.5E+11 | 5.184E+13 |
| 500,000 | 8,000,000 | 4E+12 | 2.5E+11 | 6.4E+13 |
| 660,000 | 7,500,000 | 4.95E+12 | 4.36E+11 | 5.625E+13 |
| 790,000 | 8,900.00 | 7.03E+09 | 6.24E+11 | 79210000 |
| 540,000 | 8,100,000 | 4.37E+12 | 2.92E+11 | 6.561E+13 |
| 420,000 | 5,900.00 | 2.48E+09 | 1.76E+11 | 34810000 |
| 380,000 | 4,000,000 | 1.52E+12 | 1.44E+11 | 1.6E+13 |
From the above table and formula we get the value are as;
| n | 8 |
| sum(XY) | 20853509000000 |
| sum(X) | 4190000.00 |
| sum(Y) | 40814800.00 |
| sum(X^2) | 2332100000000.00 |
| sum(Y^2) | 289700114020000 |
| b | -3.802980 |
| a | 7093660.7341 |
ycap = a + bx
ycap = 7093660.7341 - 3.802980x
when x = 315000
The best predicted sales =
7093660.7341 - 3.802980 * 315000
= 5895722.0
ycap = 7093660.7341 - 3.802980 * 315000
when ycap = 9500000
9500000 = 7093660.7341 - 3.802980 * x
3.802980 * x = 7093660.7341 - 9500000
x = -632751
orchestra answered 2 years 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.
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 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...
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,...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Merger Analysis TransWorld Communications Inc., a large telecommunications company, is evaluating the possible acquisition of Georgia...
- Journal Entries and Trial Balance Elite Realty acts as an agent in buying, selling, renting, and...
- In racket Assume that the elements of a list are indexed starting with 1. Write a...
- Describe System Development Life Cycle (SDLC) and how it is used.
- What symbolism do you find in the play,Oedipus?
- • Using the Scanner class to obtain input from the user. • Using printf to output...
- In each of the following situations, develop a tentative plan for the client. List the various...
ADVERTISEMENT