1. (24) You are condueting a study on household milk consumption, and observed n
ID: 1119348 • Letter: 1
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1. (24) You are condueting 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 Zi = weekly income in hundreds of dollars z2 family slae 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 coeficient (&) in the regression line? Briely explain each. (b) (6) Suppose b 063. Interpret this coefficient (e) (6) Suppose bo =-1.46. Interpret this oofcient. (d) (6) Suppose that 887 and R'-8126. Interpret the R·and RExplanation / Answer
a) Coefficient of x1 is expected to be Positive, because a higher income household is expected to spend more on consumption and hence, more on Milk
Coefficient of x2 is expected to be positive, as more are the members in a family, more would be their milk requirements and hence, the coefficient will be positive.
A lactose intolerant person would consume Milk and it's associated products in a limited or no amount. Thus, when the Dummy Variable takes the value 1, ie when a member of that family is lactose intolerant, the milk consumption of that family would be expected to be lower than when the dummy variable takes the value 0. Hence Coefficient of x3 would be negative.
b) This would mean that on an average, an increase in income by 100 dollars would result in an increase in milk consumption by 0.063 quarts per week
c) This would mean that on an average, families with atleast one Lactose intolerant member consume 1.46 quarts less milk per week than those who do not have a lactose intolerant member.
d) R square is higher than the adjusted R square. This is because Adjusted R square corrects for the the number of predictors in the model. Adjusted R square is always lower than R square, and it increases only if the new term improves the model more than would be expected by chance. Thus, in some sense, it punishes for adding more variables to the Regression. Hence, to compare two regressions, Adjusted R square would be a better indicator.
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