1. (4x3 + 5 = 17 points) Agricultural economists analyzed wine demand at a restaurant to
evaluate the impact of objective factors (e.g., origin, varietal), sensory descriptors, and price, on the choice of restaurant wines. The predictor variables are the wine features and the response variable is a count of the number of bottles of each wine sold in each week over the study period. Below is the coefficients table for fitting a Poisson regression model to the data.
a) The estimated coefficient for "Price" is -0.084, which means that if price increases by $1 (holding all else constant), then the natural logarithm of the expected quantity sold decreases by 0.084. Thus, expected quantity sold is multiplied by exp(-0.084) = 0.920 = 92%. Does this result agree with standard economic theory about the general relationship between demand and price? Briefly explain your answer.
b) The estimated coefficient for the "Lowest price indicator" is negative, which means that if a wine has the lowest price in its category on the menu, then the expected quantity sold is lower than other, more expensive wines (after accounting for the other predictors). [Diners could be avoiding the cheapest wine to appear more selective or magnanimous when choosing a wine.] The "By the glass indicator" has the value 1 for wines that are available for purchase by the glass. Do the results indicate that such wines tend to have higher or lower demand than wines that are only available for purchase by the bottle (after accounting for the other predictors)? Justify your answer.
c) The predictors marked in blue are indicator variables for the wine varietal, relative to the reference level "California Chardonnay." Which varietal is the most popular (after accounting for the other predictors)? Justify your answer.
d) The predictors marked in green are indicator variables for sensory descriptors listed on the menu. Which sensory descriptors tend to result in increased demand (after accounting for the other predictors)? Justify your answer.
e) Calculate the Wald Z test statistic for testing if the coefficient for "Citrus indicator" is zero. Test if the coefficient is zero using α = 0.05. Remember to write the hypotheses, test statistic, p-value, decision, and conclusion.
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