Question

Using 20 observations, the following regression output is obtained from estimating y = β₀ + β₁x + β₂d + β₃xd + ε.

	Coefficients	Standard Error	t Stat	p-value
Intercept	13.05	3.00	4.35	0.001
x	3.76	0.47	8.00	0.000
d	−4.59	3.06	−1.50	0.153
xd	1.89	0.70	2.70	0.016

a. Compute yˆy^ for x = 11 and d = 1; then compute yˆy^ for x = 11 and d = 0. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

b-1. Is the dummy variable d significant at the 5% level?

• Yes, since we reject the relevant null hypothesis.

• Yes, since we do not reject the relevant null hypothesis.

• No, since we reject the relevant null hypothesis.

• No, since we do not reject the relevant null hypothesis.

b-2. Is the interaction variable xd significant at the 5% level?

• Yes, since we reject the relevant null hypothesis.

• Yes, since we do not reject the relevant null hypothesis.

• No, since we reject the relevant null hypothesis.

• No, since we do not reject the relevant null hypothesis.

Answer 1

a)

for x=11 and d=1 ;y^ =13.05+3.76*11-4.59*1+1.89*11*1 =70.61

for x=11 and d=0 ;y^ =13.05+3.76*11-4.59*0+1.89*11*0 =54.41

b-1)since p value >0.05

• No, since we do not reject the relevant null hypothesis.

b-2)soince for interaction : p value 0.016 < 0.05

es, since we reject the relevant null hypothesis.