Question

Using 50 observations, the following regression output is obtained from estimating y = β₀ + β₁x + β₂d₁ + β₃d₂ + ε.

	Coefficients	Standard Error	t Stat	p-value
Intercept	−0.45	0.20	−2.25	0.0293
x	3.78	1.20	3.15	0.0029
d1	−11.88	16.50	−0.72	0.4752
d2	5.25	1.25	4.20	0.0001

a. Compute yˆy^ for x = 212, d₁ = 1, and d₂ = 0; compute yˆy^ for x = 212, d₁ = 0, and d₂ = 1. (Round your answers to 2 decimal places.)

	yˆy^
x = 212, d1 = 1 and d2 = 0
x = 212, d1 = 0 and d2 = 1

b-1. Interpret d₁ and d₂. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.)

• When d₁ = 1, %media:13252708883034636% is 11.88 units greater than when d₁ = 0, holding everything else constant.
• When d₂ = 1, %media:13252708883034636% is 5.25 units greater than when d₂ = 0, holding everything else constant.
• When d₁ = 1, %media:13252708883034636% is 11.88 units less than when d₁ = 0, holding everything else constant.
• When d₂ = 1, %media:13252708883034636% is 5.25 units less when d₂ = 0, holding everything else constant.

b-2. Are both dummy variables individually significant at the 5% level?

• No, none of the dummy variables are individually significant at 5% level.

• Yes, both dummy variables are individually significant at the 5% level.

• No, only the dummy variable d₂ is significant at 5% level.

• No, only the dummy variable d₁ is significant at 5% level.

Answer 1

Equation is y^ = -0.45 + 3.78(x)  -11.88(d1) + 5.25(d2)

(A) Calculation of y^ for  x = 212, d₁ = 1, and d₂ = 0

setting the given values

y^ = -0.45 + 3.78(212)  -11.88(1) + 5.25(0)

= -0.45 + 801.36 -11.88 + 0

= 789.03

So, y^ = 789.03

Calculation of y^ for  x = 212, d₁ = 0, and d₂ = 1

setting the given values

y^ = -0.45 + 3.78(212)  -11.88(0) + 5.25(1)

= -0.45 + 801.36 -0 + 5.25

= 806.16

So, y^ = 806.16

(B-1) Coefficient of d1 is -11.88, which means it will decrease the depedent variable y by 11.88 units as compared to when d1=0

Coefficient of d2 is 5.25, which means it will increase the depedent variable y by 5.25 units as compared to when d2 = 0

Therefore, option C and B are correct.

(B-2) p value corresponding to d1 is 0.4742 and d2 is 0.0001, it is clear that the p value corresponding to d2 is less than 0.05 level of signifcance.

Therefore, only d2 is significant and d1 is not significant because p value of d2 is less than 0.05 and p value of d1 is greater than 0.05

So, option C is correct.