Question

Please provide Stata commands and outputs for all relevant statistic, thank you.

1. The following data present the experience and salary structure of University of XYZ economists in 2017-2018. The variables are y = salary (thousands of dollars) x = years of experience (defined as years since receiving Ph.D.) Estimate the regression of y on x. Present all relevant statistics including Estimated coefficients, standard errors, t-statistics, R-squared, sum of squared residuals, an standard error of regression. Give reasons why the regression does or does not make sense. Calculate the residuals to see whether there are any outliers. Would you discard these observations or look for other explanations?

Data Set Below...

Y	X
77.7	3
67.7	6
100.4	7
93.2	9
99.3	10
112.4	10
100.3	12
101.3	12
90.6	13
101.5	15
90	16
98.1	16
111	16
37.5	17
100.7	17
95	18
105	18
103	19
105	19
106.5	19
92.4	20
96.8	20
93	21
94.41	22
97.7	22
91.2	23
105	25
102	26
89	30
91	32
104.3	32
106	43

Answer 1

USING EXCEL<DATA<MEGASTAT<CORRELATION/REGRESSION<REGRESSION

The output is as follows:

Regression Analysis
	r²	0.042
	r	0.204
	Std. Error	13.829
	n	32
	k	1
	Dep. Var.	Y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	248.9338	1	248.9338	1.30	.2629
Residual	5,737.5612	30	191.2520
Total	5,986.4950	31
Regression output					confidence interval
variables	coefficients	std. error	t (df=30)	p-value	95% lower	95% upper
Intercept	89.3640	5.98	14.94	0.00	77.15	101.58
X	0.3390	0.2972	1.141	.2629	-0.2679	0.9460

Observation	Y	Predicted	Residual
1	77.70	90.38	-12.68
2	67.70	91.40	-23.70
3	100.40	91.74	8.66
4	93.20	92.42	0.78
5	99.30	92.75	6.55
6	112.40	92.75	19.65
7	100.30	93.43	6.87
8	101.30	93.43	7.87
9	90.60	93.77	-3.17
10	101.50	94.45	7.05
11	90.00	94.79	-4.79
12	98.10	94.79	3.31
13	111.00	94.79	16.21
14	37.50	95.13	-57.63
15	100.70	95.13	5.57
16	95.00	95.47	-0.47
17	105.00	95.47	9.53
18	103.00	95.81	7.19
19	105.00	95.81	9.19
20	106.50	95.81	10.69
21	92.40	96.15	-3.75
22	96.80	96.15	0.65
23	93.00	96.48	-3.48
24	94.41	96.82	-2.41
25	97.70	96.82	0.88
26	91.20	97.16	-5.96
27	105.00	97.84	7.16
28	102.00	98.18	3.82
29	89.00	99.54	-10.54
30	91.00	100.21	-9.21
31	104.30	100.21	4.09
32	106.00	103.94	2.06

Answers:

Estimate the regression of y on x.

y=0.339x+89.364

Present all relevant statistics including Estimated coefficients The coefficient are 0.339

standard errors 5.98

t-statistics 1.30

R-squared 0.042

sum of squared residuals 5737.5612

an standard error of regression 0.2972

Give reasons why the regression does or does not make sense.?

The linear regression makes sense as the r- square is low this combination indicates that the independent variables((x) are correlated with the dependent variable(y). The p-value is also greater which means the model is not significant.

Calculate the residuals to see whether there are any outliers. Would you discard these observations or look for other explanations?

Yes, there is presence of outliers. With respect to regression, outliers are influential only if they have a big effect on the regression equation. Since r square is low such that there are no influential points in the residualsa(outliers).