1. Which of the three X variables is most important predictor in the model? Why did you choose this variable over the other two?

According to the multiple regression analysis

Predictor p-value

Circulation: 0.000

Income: 0.273

Male: 0.887

A p-value more than 0.05 indicates something is not significant. A p-value less than 0.05 means the result is significant. If the p-value is less than 0.01 the result is very significant. Applying that logic to the above, circulation is the only significant variable, so it must be the most important predictor in the model.

2. According to the output, what would be the eventual effect of a 1000 person increase in circulation? Give an interval estimate if possible.

The regression coefficient for circulation is 5.282. This indicates that a magazine with an extra 1,000 readers will charge an extra $5.28 (on average) for a one-page, full-color advertisement -- all else being equal.

If another magazine had the same median income and the same percent male readership but had 3,500 more people in its circulation, the ad cost would be expected to be 5.28 x 3.500 = 18.48 higher on average due to the increased circulation.

3. What cost does the model predict for an ad in the magazine Statistics and Other Torture Devices, which has a circulation of 1 million and has an audience that is 58 percent male with a median income of $32,000 per year? Give an interval estimate if possible. Note: setting up these calculations is sufficient.

COST = -8642.535 + 1.223 (INCOME) + 5.282(CIRCULATION) – 10.997 (MALE)

COST = -8642.535 + 1.223 (32000) + 5.282(1000) -10.997(.58)

COST = 35769.09

Interval estimate: 35769.09 plus or minus 13129.253

4. Regardless of your answer in part 3, suppose the calculation yields an estimated cost of $34,132. You find out that the actual cost of an ad in Statistics and Other Torture Devices is $49,000. This does not look like a particularly accurate prediction. Do you agree? Cite some specific numerical evidence in your answer.

The prediction equation has a standard error of estimate of 13129.253. This means that if the calculation yielded an estimated cost of 34132 at least two-thirds would fall below 47261.253.

That is 1700 less than the actual cost for an ad in Statistics and Other Torture Devices. But 95% of time, the cost will fall within 2 standard deviations and this estimation falls within that range. With that in mind, I agree that this does not look like a particularly accurate prediction.

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## Monday, April 12, 2010

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