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Use the data in CHARITY to answer this question. The variable respond is a dummy variable equal toone if a person responded with a contribution on the most recent mailing sent by a charitable organiza-tion. The variable resplast is a dummy variable equal to one if the person responded to the previous mailing, avggift is the average of past gifts (in Dutch guilders), and propresp is the proportion of timesthe person has responded to past mailings.$$\begin{array}{l}{\text { (i) Estimate a linear probability model relating respond to resplast and avggift. Report the results }} \\ {\text { in the usual form, and interpret the coefficient on resplast. }} \\ {\text { (ii) Does the average value of past gifts seem to affect the probability of responding? }}\end{array}$$$$\begin{array}{l}{\text { (iii) Add the variable propresp to the model, and interpret its coefficient. (Be careful here: an }} \\ {\text { increase of one in propresp is the largest possible change.) }} \\ {\text { (iv) What happened to the coefficient on resplast when propresp was added to the regression? Does }} \\ {\text { this make sense? }}\end{array}$$$$\begin{array}{l}{\text { (v) Add mailsyear, the number of mailings per year, to the model. How big is its estimated effect? }} \\ {\text { Why might this not be a good estimate of the causal effect of mailings on responding? }}\end{array}$$

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Chapter 7

Multiple Regression Analysis with Qualitative Information: Binary (or Dummy) Variables

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This is the estimation result of the linear probability model. You are asked to interpret the coefficient of the variable press. Blessed thistle is a dummy variable that takes a value of one if the person responded to previous melting. The coefficient of this variable, yeah, is 0.343 and it is significant at their 1% level. So if we hold the average give fixed, yeah, then if the person responds most recently, the probability of a current respond is estimated to be 0.344 higher. In Part two, you are asked to evaluate the variable average gift. This variable has a very small estimated coefficient, and it's P value is very close to the 10% level. We can interpret these variables as follow if average gift increased by 100 than the probability of responding. This period is Ali point 015 higher, and this variable is marginally statistically significant at the 10% level. In Part three, we're going to add a new variable prop reps into the equation. This is the regression result. Proper reps represent the proportion of time a person has responded to previous melting the coefficient of this variable is particularly large and it is also highly significant. The coefficient of this variable equals 0.747 which means that when this variable increased by 0.1, then the probability of responding when increased by almost 0.75 apart. Four. You could also notice that the coefficient of respond last has decreases from the previous equation or estimation. Yeah. Previously it was 0.334 and now it is 0.9 This makes sense because the relationship between responding currently and responding most recently should be weaker once the average response is controlled for certainly the two variables respond less and proportion of response are positively correlated in this part. We're going to add another variable males here. This variable has a reasonably large coefficient which is 0.0 62 It is also highly significant. The coefficient can be interpreted as each new mailing is estimated to increase the probability of responding Bye 0.62 Yeah. We are uncertain about the causal effect of this variable. It is Council on Lee. If this variable is totally exhaustion ist yeah, to the extent that it depends only on past gift giving as controlled for by the average gift, the most recent response and the response rate. The estimate could be a good or consistent estimate of the causal effect. But if melons are determined by other factors that are necessarily in the error term, such as income, then the estimate would be systematically biased.

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