Linear probability model, Mathematics

Pepsi:               A dummy variable where 1 denotes choice of Pepsi by the i-th customer and 0 otherwise

Price_P:           The price of a 2-liter bottle of Pepsi at the time of purchase

Price_7:           The price of a 2-liter bottle of 7-Up at the time of purchase

Price_C:           The price of a 2-liter bottle of Coke at the time of purchase

Disp_P:            A dummy variable where 1 denotes whether Pepsi was displayed at the time of purchase and 0 otherwise

The purpose of this exercise is to determine the factors that explain the choice of Pepsi over other types of colas.

  a. Using these data, estimate the probability (proportion) of a customer choosing Pepsi for (i) all cases; and (ii) for the cases where Pepsi is displayed.

  b. Assuming that a relationship exists between choosing Pepsi as the dependent variable and the rest as the independent variables, hypothesize the signs of the βk coefficients.

  c. Run 3 regressions of this relationship using a linear probability model, a logit model, and a probit model, and make a summary table including the estimated coefficients with their t/z ratios, R2, and the proportion of correct predictions coming from the 3 models.

  d. Calculate the proportion of correct predictions coming from the 3 models.

  e. Without running a significance test, evaluate the estimated coefficients.

  f.  Create a second table with the transformed coefficients of the logit and probit models to make them comparable to those of the linear probability model E.

 g. Using the 3 models, evaluate the probability of choosing Pepsi when Pepsi is displayed and when Pepsi is not displayed while the prices of all three drinks are equal at $1.50 per 2-liter bottle.

Posted Date: 2/22/2013 2:11:01 AM | Location : United States

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