Question

Using a study of 403 individuals in Texas, we find the following prediction equation for glycosolated hemoglobin (y, measured as a percent) using explanatory variables of total cholesterol (x1, measured in mg/dL), location (x2, dummy variable with values 0 = Dallas, 1 = Houston), and weight (x3, measured in pounds): yhat = 1.50 + 0.013 x1 + -0.3 x2 + 0.008 x3.

Which of the following is the most accurate interpretation of a parameter (i.e. intercept or slope) in this model? Pick one option.

a.) The difference in predicted glycosolated hemoglobin comparing Houston to Dallas is -0.3% controlling for weight and total cholesterol.

b.) For every one pound increase in weight, predicted glycosolated hemoglobin increases by 0.008% for the Dallas location.

c.) The mean total cholesterol for Houston when glycosolated hemoglobin and weight are both zero is 1.50 mg/dL.

d.) Controlling for weight, for every one mg/dL increase in cholesterol, glycosolated hemoglobin increases by 0.01%.

Answer 1

Which of the following is the most accurate interpretation of a parameter (i.e. intercept or slope) in this model? Pick one option.

Answer ) The mean total cholesterol for Houston when glycosolated hemoglobin and weight are both zero is 1.50 mg/dL.

Because the linear regression equation is yhat = 1.50 + 0.013 x1 + -0.3 x2 + 0.008 x3.

Where x1, measured in mg/dL), location (x2, dummy variable with values 0 = Dallas, 1 = Houston), and weight (x3, measured in pounds)

Hence if all the variables are held constant i.e. x1 , x2, x3 = 0 the mean Y hat = 1.50