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15-15 A real estate agent wishes to estimate the monthly rental for apartments based on the size (square feet) and the locations of the apartments. She chose the following model:
?= ??o+ ?1×1 + ?2×2 + ?
Where:
X1 = Square footage of the apartment
X2= 1=if located in town center
0= if not located in town center
The linear regression model was fitted to a sample of size 50 to produce the following regression expression.
? = 145 + 1.2×1 + 300 x2
a. Predict the average monthly rent for an apartment located it in the town center that has 1,500 square feet.
b. Predict the average monthly rent for an apartment located in the suburbs that has 1,500 square feet.
c. Interpret b2 in the context of this exercise.

15-65 Consider the following model:
? =5 + 3×1 + 5×2

a. Provide an interpretation of the coefficient of x1.
b. Is the interpretation provided in part a true regardless of the value of x2? Explain
c. Now consider the model ? = 5 +3×1 + 5×2 +4x1x2.
Give an interpretation of the coefficient of x1 when x2 = 1.
d. Repeat part c when x2 =2. Is the interpretation provided in part a true regardless of the value of x2? Explain
e. Considering your answers to parts c and d, what type of regression components has conditional interpretations?