Using the models 1-2, answer the following questions

1. What is a confidence interval? In model 1 below, calculate

• The t-value for the coefficient of renter.
• The 95% confidence interval for the coefficient of renter, where the t_0.025 ~ 1.96. Is the coefficient statistically significant?

2. Define the R² statistic.

3. In Model 1 below, we want to test the joint hypothesis that the coefficients on "Mortgage Payer", "Renter" and "Married" are jointly zero. We estimate a restricted model 2. How do we do test for the significance of the null hypothesis? Carry out this test.

Model 1.

Source	SS	Df	MS	Number of obs	2995
				F(7, 2987)	198.97
Model	15652624	7	2236089	Prob > F
Residual	33568672	2987	11238.26	R-squared
Total	49221296	2994	16439.98	Root MSE	106.01

Earnings	Coef.	Std. Err.	t	P>t	[95% Conf.	Interval]
Mortgage Payer	14.33137	4.620061	3.1	0.002	5.272548	23.39019
Renter	11.14287	5.838434
Married	9.252644	6.220546	1.49	0.137	-2.94434	21.44963
Pension Scheme Memb.	53.74266	4.625375	11.62	0	44.67342	62.8119
Years of Education	16.93454	0.798126	21.22	0	15.36961	18.49947
Years of Experience	9.021747	0.638824	14.12	0	7.769168	10.27433
Years of Experience2	-0.13793	0.012611	-10.94	0	-0.16266	-0.1132
Constant	-132.538	11.42962	-11.6	0	-154.949	-110.127

Model 2.

Source	SS	df	MS	Number of obs	2995
				F( 4, 2990)	334.94
Model	15230438	4	3807610	Prob > F	0
Residual	33990858	2990	11368.18	R-squared	0.3094
Total	49221296	2994	16439.98	Root MSE	106.62

Earnings	Coef.	Std. Err.	t	P>t	[95% Conf.	Interval]
Pension Scheme Memb.	58.09067	4.596827	12.64	0	49.0774	67.10393
Years of Education	17.63035	0.790479	22.3	0	16.08041	19.18029
Years of Experience	10.42731	0.534379	19.51	0	9.379517	11.47509
Years of Experience2	-0.16268	0.011396	-14.28	0	-0.18502	-0.14033
Constant	-139.151	11.18556	-12.44	0	-161.083	-117.219