An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (in millions of dollars) and the resulting percentage increase in sales following the campaign, were presented by the firm. Based on these data, we would compute the least-squares regression line to be y = 6.16+0.19x, with x representing campaign cost and y representing the resulting percentage increase in sales. (This line is shown below, along with a scatter plot of the data.) Campaign cost, x (in millions of dollars) 2.83 2.02 1.52 3.61 1.49 2.29 3.57 1.51 1.95 3.27 3.14 3.84 Send data to calculator V Increase in sales, y (percent) 6.57 6.49 6.46 6.85 6.54 6.52 6.82 6.29 6.77 6.48 6.93 7.03 Increase in sales (percent) Based on the firm's data and the regression line, complete the following. 6.8- 6.6- 6.4- 6.2 x x X xx 3.5 Campaign cost (in millions of dollars) (a) For these data, values for campaign cost that are less than the mean of the values for campaign cost tend to be paired with values for percentage increase in sales that are (Choose one) the mean of the values for percentage increase in sales. greater than less than (b) According to the regression equation, for an increase of one million dollars in advertising campaign cost, there is a corresponding increase of how many percent in sales? 0 S
An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (in millions of dollars) and the resulting percentage increase in sales following the campaign, were presented by the firm. Based on these data, we would compute the least-squares regression line to be y = 6.16+0.19x, with x representing campaign cost and y representing the resulting percentage increase in sales. (This line is shown below, along with a scatter plot of the data.) Campaign cost, x (in millions of dollars) 2.83 2.02 1.52 3.61 1.49 2.29 3.57 1.51 1.95 3.27 3.14 3.84 Send data to calculator V Increase in sales, y (percent) 6.57 6.49 6.46 6.85 6.54 6.52 6.82 6.29 6.77 6.48 6.93 7.03 Increase in sales (percent) Based on the firm's data and the regression line, complete the following. 6.8- 6.6- 6.4- 6.2 x x X xx 3.5 Campaign cost (in millions of dollars) (a) For these data, values for campaign cost that are less than the mean of the values for campaign cost tend to be paired with values for percentage increase in sales that are (Choose one) the mean of the values for percentage increase in sales. greater than less than (b) According to the regression equation, for an increase of one million dollars in advertising campaign cost, there is a corresponding increase of how many percent in sales? 0 S
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Transcribed Image Text:An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve
recent campaigns, including the cost of each campaign (in millions of dollars) and the resulting percentage increase in sales following the campaign, were
presented by the firm. Based on these data, we would compute the least-squares regression line to be y = 6.16+0.19x, with x representing campaign cost and
y representing the resulting percentage increase in sales. (This line is shown below, along with a scatter plot of the data.)
Campaign cost, x
(in millions of dollars)
2.83
2.02
1.52
3.61
1.49
2.29
3.57
1.51
1.95
3.27
3.14
3.84
Send data to calculator V
Increase in sales, y
(percent)
6.57
6.49
6.46
6.85
6.54
6.52
6.82
6.29
6.77
6.48
6.93
7.03
Increase in sales
(percent)
Based on the firm's data and the regression line, complete the following.
72+
7+
6.8+
6.6+
6.4+
6.2+
X
X
X
1.5 2 2.5
X
3
Xx
3.5
Campaign cost
(in millions of dollars)
X
(a) For these data, values for campaign cost that are less than the mean of the values for campaign cost tend to be
paired with values for percentage increase in sales that are (Choose one) the mean of the values for percentage
increase in sales.
greater than
less than
(b) According to the regression equation, for an increase of one million dollars in advertising campaign cost, there is a
corresponding increase of how many percent in sales?
X
5
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