1. (24) You are conducting a study on household milk consumption, and observed n
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Question
1. (24) You are conducting a study on household milk consumption, and observed n 33 different households in Los Angeles county. Let the following variables denote your observations: V Milk consumption in quarts per week #x-weekly income in hundreds of dollars family size z = a dummy variable that equals 1 if one of the members of the family is lactose intolerant, and 0 otherwise (a) (6) What do you predict would be the sign of each coefficient (b) in the regression line? Briefly explain each. (b) (6) Suppose by 063. Interpret this coefficient. (c) (6) Suppose b -1.46. Interpret this coeficient.Explanation / Answer
a. Our model is: y = b0+b1x1+b2x2+b3x3+error term
we expect b1 to be positive because as the weekly income increases, the family is more likely to buy/consume more milk. we expect b2 also to be positive because as the family size increases, more and more people now consumer milk. So, the consumption of milk rises. b3 is negative because if a family member is lactose intolerant, then he/she will not be consuming milk and thus, the consumption of milk of that household falls.
b. Holding all else constant, an additional increase in the income will lead to an increase in the consumption of milk by 0.063 quarts per week. (Since income is in hundreds of dollars, it will lead to an increase in consumption by 0.063*100 = 6.3 quarts per week)
c. Holding all else constant, if one of the family members is lactose intolerant, then the consumption of milk decreases by 1.46 quarts per week.
d. R2: The R-square tells us how much of the variation in the consumption of milk is explained by the model. Above, it means that our model explains 88.7% of the variation in consumption of milk.
The adjusted R-square, on the other hand, is simply a modified version of the R-square that adjusts for the number of explanatory variables in the model. It has the same interpretation as the R-square. Only this time, it accounts for whether or not the (added) explanatory variable improves the model. In the above question, it says that our model explains 81.26% of the variation in consumption of milk.
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