The data set is http:// 1: A researcher is interested in how variables, such as GRE (Graduate Record Exam scores), GPA (grade point average) and pres- tige of the undergraduate institution, effect admission into graduate school. The response variable, admit/dont admit, is a binary variable. Load the attached data file, binary.csv, into R and use R function str() to find out the structure of the file and function head() to view the first few rows of the data.

(a) Use xtabs() function to obtain a two-way contingency table of cat- egorical outcome and predictors we want to make sure there are not 0 cells. Use R glm (generalized linear model) function to estimate the coefficients of the logistic regression model with predictor variables gre, gpa, and as.factor(rank); i.e., treat the variable “rank” as categorical (or indicator) variable and NOT as a numerical variable. Make sure use glm() function with option family = “binomial” as it is shown in the example in class; see lecture notes for additional detail. Then use function summary() to obtain a summary of the results.

(b) (i) For every one unit change in gre, the log odds of admission (ver- sus non-admission) increases by how much? (ii) For a one unit increase in gpa, the log odds of being admitted to graduate school increases by how much? (iii) The indicator variables for rank have a slightly dif- ferent interpretation. For example, having attended an undergraduate institution with rank of 2, versus an institution with a rank of 1, how does the log odds of admission change?

(c) Use the predict() function to calculate the predicted probability of admission at each value of rank, holding gre and gpa at their means.

Problem 2:Refer to the previous problem.

(a) Use the first 200 cases of the data as a “training data” to fit the data by a logistic regression with predictor variables gre, gpa, and as.factor(rank); i.e., treat the variable “rank” as categorical (or indica- tor) variable and NOT as a numerical variable; i.e., repeating the work in part(b) in the previous problem BUT only using the first 200 cases. Then use the predict() function to calculate the predicted probability for each of the remaining 200 cases. Since we the admission status is known for each of these remaining 200 cases. Do you think the model give a good prediction? Why? Explain.

This is related to the so-called cross-validation method.

(b) Repeat part (b) but use the first 300 cases as “training data”. Then use the fit to predict the remaining 100 cases. Do you think the model give a good prediction? Why? Explain.

(c) Compare the results from parts (a) and (b). Explain your findings.

1 – The following table summarizes the short-run production function for your firm. Your product sells for $5 per unit, labor costs $5 per unit, and the rental price of capital is $20 per unit. Complete the following table, and then answer the accompanying questions.a. Which inputs are fixed inputs? Which are the variable inputs?b. How much are your fixed costs?c. What is the variable cost of producing 20 units of output?d. How many units of the variable input should be used to maximize profits?e. What are your maximum profits?f. Over what range of variable input usage do increasing marginal returns exist?g. Over what range of variable input usage do decreasing marginal returns exist?h. Over what range of variable input usage do negative marginal returns exist? 2 – Based on your knowledge of one-shot and repeated games, would you expect tipping behavior to differ depending on whether a person is eating in a hometown diner or in a restaurant located in Timbuktu? Explain. JVC’s objective is to maximize revenues, and it is considering three strategies to price its stereo components: (1) a standard strategy whereby it prices each stereo component separately; (2) perfect price discrimination; or (3) bundling the three components together and selling only bundles containing the receiver, CD player, and speakers.a. If JVC uses a standard pricing strategy, what price should it charge for the receiver, for the CD player, and for the speakers to maximize revenues? What are the revenues they will earn through this strategy?b. Suppose JVC adopts a first-degree price discrimination policy. What prices should it charge to maximize revenues? What are JVC’s revenues using this strategy?c. Suppose that JVC markets the receiver, CD player, and speakers together. That is, it uses a commodity-bundle strategy such that the products are sold as one item. What price should JVC charge to maximize revenues? How much will it earn?