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 (denoted by x, in millions of dollars) and the resulting percentage increase in sales (denoted by y) following the campaign, were presented by the firm. A scatter plot of the data is shown in Figure 1. Also given is the product of the campaign cost and the percentage increase in sales for each of the twelve campaigns. (These products, written in the column labelled "xy", may aid in calculations.) Campaign cost, x (in millions of dollars) Increase in sales, y (percent) xy 4.01 7.01 28.1101 3.31 6.57 21.7467 3.59 6.81 24.4479 2.30 6.53 15.019 1.50 6.22 9.33 1.29 6.40 8.256 2.02 6.51 13.1502 2.15 6.78 14.577 3.07 7.02 21.5514 1.50 6.67 10.005 3.63 6.70 24.321 2.98 6.56 19.5488 Send data to calculator Increase in sales (percent) y 6 6.2 6.4 6.6 6.8 7 7.2 x 1 1.5 2 2.5 3 3.5 4 Campaign cost (in millions of dollars) Figure 1 What is the sample correlation coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places.

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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Question

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 (denoted by x, in millions of dollars) and the resulting percentage increase in sales (denoted by y) following the campaign, were presented by the firm. A scatter plot of the data is shown in Figure 1. Also given is the product of the campaign cost and the percentage increase in sales for each of the twelve campaigns. (These products, written in the column labelled "xy", may aid in calculations.)

Campaign cost, x (in millions of dollars)	Increase in sales, y (percent)	xy
4.01	7.01	28.1101
3.31	6.57	21.7467
3.59	6.81	24.4479
2.30	6.53	15.019
1.50	6.22	9.33
1.29	6.40	8.256
2.02	6.51	13.1502
2.15	6.78	14.577
3.07	7.02	21.5514
1.50	6.67	10.005
3.63	6.70	24.321
2.98	6.56	19.5488

Send data to calculator

Increase in sales
(percent)

6.2

6.4

6.6

6.8

7.2

1.5

2.5

3.5

Campaign cost
(in millions of dollars)

Figure 1

What is the sample correlation coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places.

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