Problem(1):
You are given the following estimated regression
equation involving a dependent and two
independent
variables:
ŷ = 22.8 + 19x1 + 5.56x2
a. Interpret the values of the slope coefficients in
the equation.
b. Estimate the value of the dependent variable
when x1 = 10 and x2 = 5.
Problem(2):
Consider the following regression model:
y = b0 + b1x1 + b2x2 + ε
where:
x1 = a quantitative variable
x2 = 1 if x1<40
x2 = 0 if x1>=40
Assume the estimated regression equation is :
ŷ = 30.5 + 2.1 x1 + 6.3 x2
a. Provide the estimated regression equation for
instances in which x1 < 40.
b. Determine the value of y when x1 = 20.
c. Provide the estimated regression equation for
instances in which x1 > 40.
d. Determine the value of y when x1 = 55.
Answers(1):
a. b1 = 19. This implies that, holding x2 constant
and increasing x1 by one unit, the average y is
estimated to increase by 19 units.
b2 = 5.56. This implies that, holding x1
constant and increasing x2 by one unit, the
average y is estimated to increase by 5.56 units.
b. yö =22.8 + 19(10) +5.56(5) =240.6
Answers(2):
a.
b.
c.
d.
yˆ = 30.5 + 2.1x1 + 6.3(1) = 36.8 + 2.1x1
yˆ = 30.5 + 2.1(20) + 6.3(1) = 78.8
yˆ = 30.5 + 2.1 x1 + 6.3(0) = 30.5 + 2.1x1
yˆ = 30.5 + 2.1(55) + 6.3(0) = 146