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 3 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)
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16
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(b) Use the method of least squares to compute an estimated
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The following data represent a company's yearly sales volume and its advertising expenditure over a period...
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company's yearly sales volume and its advertising expenditure over
a period of 8 years.
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Advertising ($10,000)
15
32
16
33
18
35
17
34
16
36
19
37
19
39
24
42
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15 32
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advertising.
(b) Use the method of least squares to compute an estimated
regression line between sales and advertising by computing b0...
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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
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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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