# Question: Initial levels of advertising often bring a larger response in

Initial levels of advertising often bring a larger response in the market than later spending. In this example, advertising comes in the form of devoting more shelf space to the indicated product. The level of sales is the weekly total sales of this product at several outlets of a chain of markets. The display space gives the number of shelf feet used to display the item. The data include sales at 48 stores.

(a) Create a scatterplot for the level of sales on the number of shelf feet. Does the relationship appear linear? Do you think that it ought to be linear?

(b) Fit a linear regression equation to the data, regressing sales on the number of shelf feet. Does this fitted model make substantive sense?

(c) Consider a scatterplot that shows sales on the log of the number of shelf feet. Does the relationship seem more linear than in part (a)?

(d) Fit a regression of sales on the log of the number of shelf feet. Does this model provide a better description of the pattern in the data? What do the slope and intercept tell you?

(e) Compare the ft of the two models to the data. Can you rely on summary statistics like r2 and se?

(a) Create a scatterplot for the level of sales on the number of shelf feet. Does the relationship appear linear? Do you think that it ought to be linear?

(b) Fit a linear regression equation to the data, regressing sales on the number of shelf feet. Does this fitted model make substantive sense?

(c) Consider a scatterplot that shows sales on the log of the number of shelf feet. Does the relationship seem more linear than in part (a)?

(d) Fit a regression of sales on the log of the number of shelf feet. Does this model provide a better description of the pattern in the data? What do the slope and intercept tell you?

(e) Compare the ft of the two models to the data. Can you rely on summary statistics like r2 and se?

## Answer to relevant Questions

Cars depreciate over time. These data show the prices of Honda Accords listed for sale by individuals in The Philadelphia Inquirer. One column gives the asking price (in thousands of dollars) and a second column gives the ...These data give the gross domestic product (a measure of the size of a national economy, in billions of dollars) and the amount of CO2 (carbon dioxide, in millions of tons) released into the atmosphere in 140 countries in ...This figure shows an estimated linear equation with 95% prediction intervals. Assume that the units of X and Y are dollars. (a) Visually estimate the intercept b0 and the slope b1. (b) Is se (b1) less than 1, about 1, or ...This data table contains the listed prices and weights of the diamonds in 48 rings offered for sale in The Singapore Times. The prices are in Singapore dollars, with the weights in carats. Formulate the regression model with ...A firm that operates a large, direct-to-consumer sales force would like to put in place a system to monitor the progress of new agents. A key task for agents is to open new accounts; an account is a new customer to the ...Post your question