Question

While browsing through a magazine rack at a bookstore, a statistician decides to examine the relationship between the price of a magazine and the percentage of the magazine space that contains advertisements. The data are given in the following table.

Percentage containing ads	37	43	58	49	70	28	65	32
Price ($)	5.50	6.95	4.95	5.75	3.95	8.25	5.50	6.75

a. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between the percentage of a magazine's space containing ads and the price of the magazine?

Yes.

No.

b. Find the estimated regression equation of price on the percentage of space containing ads. Round your answers to four decimal places. y^=+()x

c. Interpret the meaning of the values of a and b calculated in part b. a is the change in the average price of the magazine per one percent increase in space for containing ads.change in ad space required to increase the price of the magazine by one dollar.percent of ads necessary to have a free magazine.price of a magazine with zero percent of the space containing ads. b is the change in ad space required to increase the price of the magazine by one dollar.percent of ads necessary to have a free magazine.price of a magazine with zero percent of the space containing ads.change in the average price of the magazine per one percent increase in space for containing ads.

d. Choose the plot of the the predictive regression line on the scatter diagram of part a, and show the errors by drawing vertical lines between the scatter points and the predictive regression line.

e. Predict the price of a magazine with 50% of its space containing ads. Round your answer to two decimal places. $ the tolerance is +/-2%

f. Estimate the price of a magazine with 97% of its space containing ads. Round your answer to two decimal places. $ Why should we have little confidence in this estimate? Answers: The regression model is based on data for magazines with ad space ranging from 28% to 70%. The regression model does not take into consideration the articles in the magazine. The regression model is based on estimates of the ad space percentages.It is unrealistic to find a magazine with 97% of its space filled with ads. The sample of magazines was too small to create an accurate model. the tolerance is +/-2%

Answer 1

a) Yes (in fact, negative, linear association)

b) y^=9.3898+(-0.0720)*x

c) a is price of a magazine with zero percent of the space containing ads.

b is  change in the average price of the magazine per one percent increase in space for containing ads.

d)

errors are indicated by bold black lines

e) Predicted price=5.79

f) Predicted price=2.41

The regression model is based on data for magazines with ad space ranging from 28% to 70%.

For any query in above, comment.