Question

Please provide the Stata commands and outputs where necessary, thank you.

4. The following are data on

y = quit rate per 100 employees in manufacturing

x = unemployment rate

The data are for United States and cover the period 1990-2002.

Year	Y	X
1990	1.3	6.2
1991	1.2	7.8
1992	1.4	5.8
1993	1.4	5.7
1994	1.5	5.0
1995	1.9	4.0
1996	2.6	3.2
1997	2.3	3.6
1998	2.5	3.3
1999	2.7	3.3
2000	2.1	5.6
2001	1.8	6.8
2002	2.2	5.6

(a) Estimate the regression and report the results

(b) Construct a 95% confidence interval for β.

(c) Test the hypothesis H₀ : β = 0 against the alternative β=0 at the 5% significance level.

(d) Test Normality of the residuals using Jarque-Bera test.

(e) What is likely to be wrong with the assumptions of the classical normal linear model in this case? Discuss.

Answer 1

Answer:

Given Data,

The following are data on

y = quit rate per 100 employees in manufacturing

x = unemployment rate

The data are for United States and cover the period 1990-2002.

Year	Y	X
1990	1.3	6.2
1991	1.3	7.8
1992	1.4	5.8
1993	1.4	5.7
1994	1.5	5.0
1995	1.9	4.0
1996	2.6	3.2
1997	2.3	3.6
1998	2.5	3.3
1999	2.7	3.3
2000	2.1	5.6
2001	1.8	6.8
2002	2.2	5.6

(a).To find the regression and report the results:

Modify table shown below,

Y	X	Y2	X2	XY
1.3	6.2	1.69	38.44	8.06
1.2	7.8	1.44	60.84	9.36
1.4	5.8	1.96	33.64	8.12
1.4	5.7	1.96	32.49	7.98
1.5	5.0	2.28	25.00	7.50
1.9	4.0	3.61	16.00	7.60
2.6	3.2	6.76	10.24	8.32
2.3	3.6	5.29	12.96	8.28
2.5	3.3	6.25	10.89	8.25
2.7	3.3	7.29	10.89	8.91
1.8	6.8	3.24	46.24	12.24
2.2	5.6	4.84	31.36	13.32
Y=24.9	X=65.9	Y2=50.99	X2=360.35	XY=118.7

To find a:

To find b:

(b).To construct a 95% confidence interval for :

Construct a 95% confidence interval for β.

95% CI for β

(c) To test the hypothesis H₀ : β = 0 against the alternative β=0 at the 5% significance level:

H₀ : β=0 VSH₁: β 0 at 5%

p-value is 0.001<0.05

This result is significant. So we reject the null hypothesis.

Using R Programming:

(d) To test Normality of the residuals using Jarque-Bera test:

From JB test

p= 0.224>0.05

That is follow normality

(e).What is likely to be wrong with the assumptions of the classical normal linear model in this case? Discuss:

If X or Y from the data to be analyzed by simple regression model were sample violate one or more of the regression assumption when the our result of analysis be incorrect.