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	10.24	3.20	3.20	0.006
x	3.25	0.52	6.25	0.000
d	−6.93	4.62	−1.50	0.153
xd	3.60	0.60	6.00	0.000

a. Compute yˆ for x = 10 and d = 1; then compute yˆ for x = 10 and d = 0. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

x = 10 and d = 1	yˆ=
x = 10 and d = 0	yˆ=

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

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

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

• Yes, since we 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

Solution-A:

y^=10.24+3.25*x1-6.93d+3.60xd

For

x = 10 and d = 1

y^=10.24+3.25*x1-6.93d+3.60xd

=10.24+3.25*10-6.93*1+3.60*10*1

y^=71.81

For

x = 10 and d = 0

y^=10.24+3.25*10-6.93*0+3.60*10*0

=42.74

x = 10 and d = 1	yˆ=71.81
x = 10 and d = 0	yˆ= 42.74

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

p=0.153

p>0.05

Do not reject Ho

Not significant

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

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

p=0.000

p<0.05

reject Ho

significant

Yes, since we reject the relevant null hypothesis.