Question #24 / 25 An advertising firm wishes to demonstrate to its clients the e

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Question #24 / 25 An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on fifteen 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 6.17+0.17x, with x representing campaign cost and y representing the resulting percentage increase in sales. (This line is shown in Figure 1, along with a scatter plot of the data.) Campaign cost, x Increase in sales, (in millions of dollars) 1.93 1.64 3.99 3.29 1.68 2.22 2.46 3.67 3.05 1.50 2.95 3.48 (percent) 6.47 6.70 7.00 6.48 6.20 6.73 6.56 6.75 6.84 6.41 6.58 6.78 7.2 6.8 6.6 6.4 6.2 15223 3 354 Figure 1

Explanation / Answer

Here dependent variable (y) is increase in sales and independent variable is compgain cost (x).

The regression equation is,

y^ = 6.17 + 0.17x

According to the regression equation for an increase of one million dollars in advertising compaign cost there is a corresponding increase of 0.17 percent in sales.

Now we have to find y when x = 1.50 million dollars

y^ = 6.17 + 0.17*1.50 = 6.425 percent

There is positive relationship between x and y.

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