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Use the data in CHARITY to answer the following questions:(i) Estimate the equation$$g i f t=\beta_{0}+\beta_{1} \text { mailsyear }+\beta_{2} \text { giftlast }+\beta_{3} \text { propresp }+u$$by OLS and report the results in the usual way, including the sample size and $R$ -squared.How does the $R$ -squared compare with that from the simple regression that omits giftlast andpropresp?(ii) Interpret the coefficient on mailsyear. Is it bigger or smaller than the corresponding simpleregression coefficient?(iii) Interpret the coefficient on propresp. Be careful to notice the units of measurement of propresp.(iv) Now add the variable avggift to the equation. What happens to the estimated effect of mails-year?(v) In the equation from part (iv), what has happened to the coefficient on giftlast? What do youthink is happening?

(i) Higher (ii) smaller (iii) see video (iv) smaller (v) see video

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Chapter 3

Multiple Regression Analysis: Estimation

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Sam B.

October 12, 2021

When putting this into stata how do I show the .1 increase in propresp? I have the same question for my class but have to prove it using stata.

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Part one. This is the estimated equation. We have 4,268 observations and the R Square is .08. These are square is likely higher than the R square of the simple regression, which is a point 014 It seems that adding two new variables, Gift last and proportion of response helps the model explain substantially more variations in gifts are too holding two variables gift less and proportionate response fixed one more. Melling per year is expected to increase the number of gifts by two points 17 Golders from the simple regression. The estimate is two points 65 or three. This variable is a proportion. So we when we interpret this variable, we would we wouldn't talk about a change of Ah let's see .1, not a unit increase because it makes little sense for these variables do Increased by one. That means It goes from 0 to 1 8.1 or a 10 point increase in this variable leads to a increase, an increase in gifts bye one x 4 golders. This is a product of 15 point 36 and going once 10% point are for this is the estimated equation. We have one more variable average gift. After controlling for the average past gift level, the effect of mailings becomes smaller, 1.2 Golders, less than half of the effect estimated by the simple regression our side after controlling for the average past gifts, we find that the current gift amount is negatively related to the most recent gift. This makes sense because people might follow a large donation with a smaller one.

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