Question

Consider a linear regression model where y represents the response variable, x is a quantitative explanatory variable, and d is a dummy variable. The model is estimated as  yˆy^  = 15.4 + 3.6x − 4.4d.

a. Interpret the dummy variable coefficient.

• Intercept shifts down by 4.4 units as d changes from 0 to 1.

• Slope shifts down by 4.4 units as d changes from 0 to 1.

• Intercept shifts up by 4.4 units as d changes from 0 to 1.

• Slope shifts up by 4.4 units as d changes from 0 to 1.

b. Compute y^ for x = 3 and d = 1. (Round your answer to 1 decimal place.)

y^ = _________

c. Compute y^  for x = 3 and d = 0. (Round your answer to 1 decimal place.)

y^ = _________________

Answer 1

Solution:-

Given data:-

The linear regression line, y^  = 15.4 + 3.6 x − 4.4 d

Consider x and d are the explanatory variables in the same way assume that the response variable is y

(a)

As d=1 means  − 4.4 is the dummy variable

Intercept shifts down by 4.4 units as d changes from 0 to 1

As d=0 means  − 4.4 is the dummy variable

Slope shifts down by 4.4 units as d changes from 0 to 1

Options a and b are correct.

(b)

y^  = 15.4 + 3.6 x − 4.4 d

x = 3 and d = 1

y^  = 15.4 + 3.6 (3) − 4.4 (1)

y^  = 15.4+10.8-4.4

y^  = 21.8

(c)

y^  = 15.4 + 3.6 x − 4.4 d

x = 3 and d = 0

y^  = 15.4 + 3.6 (3) − 4.4 (0)

y^  = 15.4+10.8

y^  = 26.2