Question

Du Lissuil Aug 19, 2019 1. List the variables Sales and Ads in the data file salad.xlsx on the LMS networks. Sales is the number of boxes of Cheerios sold by Kellogs during 12 sample periods and Ads is the expenditure on Cheerios advertising in million real US dollars. (a) Scatterplot Sales versus Ads. Please discuss the plot briefly. (b) Fit the following linear regression model by using the command Im( sales ads) in R. Sales, = Bo + B; Ads, + (c) What factors might influence the error terms ei? (d) Based on your estimates, what is the predicted number of boxes of Cheerios that Kellogs would sell if it decided to do no advertising. Do you believe this prediction? What might be the problem? (e) Suppose that Kellogs makes a profit of 75 cents on each box of cereal that it sells. Should it be advertising? Why or why not? (f) What is the sum of the residuals from your estimated model? (g) Is this model is good one? why or why not?

Answer 1

(a) Scatterplot Sales versus Ads.

Load the data into Excel.

Go to Data>Megastat.

Select the option Correlation/Regression and go to Scatterplot.

Select Sales as the horizontal axis.

Select Ads as the vertical axis.

Click OK.

The output will be as follows:

We can see from the Scatterplot that there is a positive linear relationship between Sales and Ads. For every one dollar increase in Sales, Ads cost will increase by 0.501 dollars.

(b) Fit the linear regression model.

A simple linear regression equation has a form:

y = b₀ + b₁*x

We have our simple linear regression equation:

y = 39.788 + 0.501*x

Or

Ads = 39.788 + 0.501*Sales

(c) What factors might influence the error terms?

An error term represents the margin of error within a statistical model; it refers to the sum of the deviations within the regression line, which provides an explanation for the difference between the results of the model and actual observed results. Therefore, the deviation will influence the error terms which in our scatterplot is not influenced.

(d) What is the predicted number of boxes of Cheerios that Kellogs would sell if it is decided to do no advertising?

The regression equation is:

Ads = 39.788 + 0.501*Sales

If Ads = 0, then

0 = 39.788 + 0.501*Sales

0.501*Sales = -39.788

Sales = -79.417

which is not possible because sales cannot be a negative term. So, we do not believe this prediction because sales cannot be a negative quantity.

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