Based on the firm's data and the regression line, complete the following.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 (greater than) or (less than) the mean of the values for percentage increase in sales.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? An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelverecent campaigns, including the cost of each campaign (in millions of dollars) and the resulting percentage increase in sales following the campaign, werepresented 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 costand 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)3.694.042.083.161.232.163.053.123.661.662.401.68Increase in sales, y(percent)6.757.036.536.976.386.826.526.486.926.596.716.24Increase in sales(percent)7.2+7+6.86.66.4-6.26+1.5XXXX2.5X3.5Campaign cost(in millions of dollars)XX*

The slope is 0.19 and it is positive.

Answered: Based on the firm's data and the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Based on the firm's data and the regression line, complete the following.

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 (greater than) or (less than) the mean of the values for percentage increase in sales.

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?

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)
3.69
4.04
2.08
3.16
1.23
2.16
3.05
3.12
3.66
1.66
2.40
1.68
Increase in sales, y
(percent)
6.75
7.03
6.53
6.97
6.38
6.82
6.52
6.48
6.92
6.59
6.71
6.24
Increase in sales
(percent)
7.2+
7+
6.8
6.6
6.4-
6.2
6+
1.5
X
X
X
X
2.5
X
3.5
Campaign cost
(in millions of dollars)
X
X
*

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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