You are conducting a study on household milk consumption, and observed n = 33 di
ID: 1217293 • Letter: Y
Question
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: y = Milk consumption in quarts per week x_1 = weekly income in hundreds of dollars x_2 = family size x_3 = a dummy variable that equals 1 if one of the members of the family is lactose intolerant, and 0 otherwise What do you predict would be the sign of each coefficient (b-1) in the regression line? Briefly explain each. Suppose b_1 =_063_Interpret this coefficient. Suppose b_3 = -1.46. Interpret this coefficient. Suppose that R^2 = .887 and R^2 = .8126. Interpret the R^2 and R^overbar^2.Explanation / Answer
a. b 1 is the coefficient of x1 in the regression equation which denotes weekly income. Since milk is a normal good, any increase in the income of the households will increase consumption of milk. Thus, b 1 will be of positive sign.
b. If b 1 = .063, it means that increase in the income of the households by 1 unit , will leads to increase in the units of milk consumed by .063 units, keeping all the other variables constant.
c. If b3 = -1.46, it means that if one of the members of the family is lactose intolerant, then the consumption of milk will fall by 1.46 units.
d. r Squared of 0.887 indicates that 88.7 per cent of the variation in milk consumption is explained by income of the households, family size and lactose intolerance of the households.
Adjusted R Squared takes into consideration only those variables out of the three mentioned above, that actually are significant in determining milk consumption of the households. Thus, it is generally lower than R Squared. In this case the independent variables explain 81.26 per cent of the variation in the milk consumption.
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