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Performing and Interpreting Results in a Simple Regression

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Your company maintains a corporate website, which is managed for it by an independent company ("Webmedia"). They suggest to you that you should pay to advertise your website on one of the most widely visited sites on the web, site W. As proof that this is worthwhile they give you numbers from another (anonymous) client, corporation X, showing the number of "hits" per week over a period of twenty weeks, during some of which they advertised their own site at site W. This data is contained in the dataset website.dta from the data archive. The column "hits" gives the number of hits per week, and the column "advatW" contains a 0 for weeks when the site was not advertised at W, and a 1 for weeks when it was.

Your first step is to regress the number of hits on the advertising dummy.

(a) Based on this regression, how many extra hits do you estimate you will get by advertising your site at site W?
(b) Give a 90% confidence interval for this number (of extra hits).
(c) Can you think of any reason you might not trust this confidence interval as a prediction of your extra hits? (i.e. why your actual confidence could be less than 90%?)
(d) Suppose now that your company has decided to value each hit at 1 cent. You are being offered a contract for an initial ten weeks of advertising space at $2,000 per week. Using your regression model, can you prove that buying the advertising would be profitable, at the significance level .05? Use the "klincom" command and answer with a formal hypothesis test.
(e) Would you in fact buy the advertising? Why might you give an answer here which is contrary to the answer in (d)?

hits advatW
1 331100 1
2 98457 0
3 247150 0
4 111540 1
5 371630 1
6 185060 1
7 515440 1
8 24040 0
9 280150 1
10 288230 0
11 217730 0
12 253800 0
13 238290 1
14 276270 1
15 71230 0
16 283670 1
17 37841 0
18 425950 1
19 101140 1
20 45186 1.

Solution Preview

Please check attachment.

(a) Based on this regression, how many extra hits do you estimate you will get by advertising your site at site W?
We first run the regression in excel. From the excel result, there are 108976 extra hits we will get by advertising site our site at site W.

(b) Give a 90% confidence interval for this number (of extra hits.)
From excel result, the 90% confidence interval for this number is [8183, 209768]

(c) Can you think of any reason you might not trust this confidence interval as a ...

Solution Summary

The solution gives detailed steps on performing and interpreting results in a simple regression using a real case.

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