Question

Company A is a microcomputer producer. The following data represents Company A’s yearly sales volume and its advertising expenditures over a period of 8 years. Sales in millions of dollars and advertising is in $10,000.

1993 15 32
1994 16 33
1995 18 35
1996 17 34
1997 16 36
1998 16 36
1999 19 39
2000 24 42

Using the method of least squares, what is the estimated regression line between sales and adverting, and the predicted sales in dollars, whth an advertising expenditure of $400K actual dollars as scaled to 40.

a. Sales=-10.4211 =.7895 Advertising: Sales $315,790
b. Advertising= 16.7143 + 1.0714 Sales: Sales $59.57 Million
c. Sales=.7895 + 10.421 Advertising: Sales $416.63 Million
d. Sales= -10.4211 + .7895 Advertising: Sales= $21.16 Million
e. None of the Above

Answer 1

Answer on Question #41806, Math, Statistics and Probability

Company A is a microcomputer producer. The following data represents Company A's yearly sales volume and its advertising expenditures over a period of 8 years. Sales in millions of dollars and advertising is in $10,000.

1993 15 32

1994 16 33

1995 18 35

1996 17 34

1997 16 36

1998 16 36

1999 19 39

2000 24 42

Using the method of least squares, what is the estimated regression line between sales and advertising, and the predicted sales in dollars, with an advertising expenditure of $400K actual dollars as scaled to 40.

a. Sales = -10.4211 = .7895 Advertising: Sales $315,790

b. Advertising = 16.7143 + 1.0714 Sales: Sales $59.57 Million

c. Sales = .7895 + 10.421 Advertising: Sales $416.63 Million

d. Sales = -10.4211 + .7895 Advertising: Sales = $21.16 Million

e. None of the Above

Solution

Calculate the slope.

$$m = \frac {\sum x y - \frac {(\sum x) (\sum y)}{n}}{\sum x ^ {2} - \frac {(\sum x) ^ {2}}{n}} = \frac {5 1 1 7 - \frac {2 8 7 \cdot 1 4 1}{8}}{1 0 3 7 1 - \frac {2 8 7 ^ {2}}{8}} = \frac {5 8 . 6 2 5}{7 4 . 8 7 5} = 0. 7 8 3 0.$$

Calculate the y-intercept.

$$b = \frac {\sum y}{n} - m \cdot \frac {\sum x}{n} = \frac {1 4 1}{8} - 0. 7 8 3 \cdot \frac {2 8 7}{8} = - 1 0. 4 6 5 1.$$

Thus

$$\text{Sales} = -10.4651 + 0.7830 \cdot \text{Advertising}.$$ $$\text{Sales} \ (40) = -10.4651 + 0.7830 \cdot 40 = \$20.85 \ \text{Million}.$$

Answer: e. None of the Above.

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