Question

A group of high-technology companies agreed to share employee salary information in an effort to establish salary ranges for technical positions in research and development. Data obtained for each employee included current salary (Salary), an indicator variable indicating highest academic degree obtained (Degree - O for an employee with a master degree and Degree - 1 for an employee with a Ph.D. degree), and years of experience since last degree (Years). The data are provided in an Excel file "Final (DATA) Salary A multiple regression model is suggested as follows: Salary = Bo + B. Degree + B Years + B, Degree. Years +6 Run the above regression model and answer the following questions: 1. Find the proportion of variation in Salary explained by the regression model Choose) > 2. Find the value of the interaction between Degree and Years. [Choose 3. How much increase in Salary is expected per each additional year of experience for an employee with a master degree? [Choose) 4. How much increase in Salary is expected per each additional year of experience for an employee with a Ph.D. degree? [Choose 5. Find the difference between the starting salary of an employee with a PhD degree and that of an employee with a master degree. Choose 6. Predict the average salary of an employee with a Ph.D. degree and 5 years (Choose] of experience > Choose 7. Find the margin of error associated with a 95% prediction interval for the salary of an employee with a Ph.D. degree and five years of experience. Use an approximate formula

Answer 1

using excel>addin>phstat>Regression>multiple regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.9730
R Square	0.9468
Adjusted R Square	0.9424
Standard Error	11527.0654
Observations	40
ANOVA
	df	SS	MS	F	Significance F
Regression	3	85137398343.5194	28379132781.1731	213.5805	0.0000
Residual	36	4783436505.8556	132873236.2738
Total	39	89920834849.3750
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	89564.1788	9948.5736	9.0027	0.0000	69387.5365	109740.8211
degree	43807.8159	13712.9003	3.1946	0.0029	15996.7653	71618.8664
years	6842.9096	1054.1825	6.4912	0.0000	4704.9284	8980.8909
degree*yeears	3794.3966	1439.6396	2.6357	0.0123	874.6722	6714.1210

Confidence Interval Estimate and Prediction Interval
Data
Confidence Level	95%
	1
degree given value	1
years given value	5
degree*yeears given value	0
X'X	40	20	367.5	185.2
	20	20	185.2	185.2
	367.5	185.2	3634.41	1853.18
	185.2	185.2	1853.18	1853.18
Inverse of X'X	0.744876	-0.74488	-0.07623	0.076234
	-0.74488	1.415211	0.076234	-0.14323
	-0.07623	0.076234	0.008364	-0.00836
	0.076234	-0.14323	-0.00836	0.015598
X'G times Inverse of X'X	-0.38117	1.051506	0.041818	-0.10881
[X'G times Inverse of X'X] times XG	0.879425
t Statistic	2.028094
Predicted Y (YHat)	167586.5
For Average Predicted Y (YHat)
Interval Half Width	21923.31
Confidence Interval Lower Limit	145663.2
Confidence Interval Upper Limit	189509.9
For Individual Response Y
Interval Half Width	32049.36
Prediction Interval Lower Limit	135537.2
Prediction Interval Upper Limit	199635.9

Ans 1 ) 0.9468

Ans 2 ) 0.0123

Ans 3 ) 0

ANs 4 ) 43807.8159

ANs 5 ) 43807.8159

ANs 6 ) 167586.5

Ans 7 ) 32049.36