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# Logistic regression: Interpretation of computer output

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In this problem, the computer output from a logistic regression analysis is provided. We are asked to provide the following:

a) Test the model significance at the .05 level.
b) State the null and alternative hypothesis, the p-value and the decision from the hypothesis test.
c) State the estimated regression equation.
d) Compute the odds ratio for one of the variables.
e) Interpret output regarding the Wald Chi Square statistic.
f) Interpret model parameter estimates.
g) Interpret an alternative model using dummy variables

The output below is from a logic regression. The dependent variable is wheather or not someone placed an order from a particular catalog. Two predictor variables were used, recency (years since the most recent purchase) and freq (number of previous orders). Neither variable has extreme outliers. Answer the questions below.

a) Test the overal significance of the model at the .05 level. State the null and alternative hypothesis, the P-value, and your decision.
b) State the estimated regression equation.
c) Compute the "Odds ratio" value for the recency variable.
d) What is the null and alternative hypothesis that the "Wald Chi-Square" statistic and "Pr > ChiSq" columns allow you to test?
e) The interpretation of the parameter estimate for freq is (0.2048), for every additional order, on average (choose the best answer).
i. the log-odds ratio (of response) increaases by 0.2048.
ii. the log-odds ratio (of response) is multiplied by 0.2048.
iii. the odds (of response) increase by 0.2048.
iv. the odds (of response) are multiplied by 0.2048.
f) Suppose that person A has made four previous purchases and that person B hasmadeonly one. Both people have the same value of recency. How do the odds(not log odds) of response compare? That is, how much more/less likely(in terms of odds) is person A to respond than person B?
g) Compute the estimated probability of response for a customer who has recency = 1 year and freq = 2 times.
h) Three dummy variables were added to this model and all the parameters were estimated. The fit statistics are given below (attached). Does the new model give a better fit than the previous one? Which numbers do you loook at to make this decision? (If you want to do a likelihood ratio test, the 95th percentile of a Chi-Square distribution with 3 degrees of freedom is 7.815.)