Question

A linear relationship of Wage with Education (Educ), Experience (Exper) and Tenure with the current employer is given by the following equation:

Expendi=β0+β1Educi+β2Experi+β3Tenurei+ui,Expendi=β0+β1Educi+β2Experi+β3Tenurei+ui,

The estimated multiple regression model is given below with some missing quantities.

• Fill in the missing quantities highlighted in blue colour in the SUMMARY OUTPUT table below.

• Answer the following (use the dropdown menu where required!)

  1. After computing the value of the F-statistic and the upper 5% critical value, we can infer about the test of the overall goodness of fit. Our decision is AnswerThe model does not have utilityInconclusiveWe should use t-test statistic here to test the overall goodness of fitThe model is useful for prediction.
  2. The coefficient of education can be interpreted as AnswerHolding the years of experience, education and tenure constant, a worker with an additional year of education has a higher income by $5.28 per hourHolding the years of experience and tenure constant, a worker with an additional year of education has a higher income by $5.28 per hourA worker with an additional year of education has a higher income by $5.28 per hour, on average.Holding the years of experience and tenure constant, a worker with an additional year of education has a higher income by $5.28 per hour, on average.
  3. The predicted wage of a person with 16 years of education, 7 years of experience and 4 years tenure is Answer
  4. Based on the value of the JB-statistic, our decision is to Answerreject the null of normally distributed errorsmaintain the null of normally distributed errors
  5. The 95% confidence interval for the coefficient of Education is interpreted as Answerwe are 95% confident that the true impact of an additional year of education increases the wage somewhere between $1.02 and $9.53, holding all else equalThere is 95% chance that the true impact of an additional year of education increases the wage somewhere between $1.02 and $9.53, holding all else equal
  6. To test a hypothesis on the individual regression, the distribution of the t-test statistic is AnswerChi-Square distributionapproximately standard normalF-distribution

SUMMARY OUTPUT
Regression Statistics			Normality Testing
Multiple R	0.672		Skewness (S)		1.351
R-Square	0.451		Kurtosis (K)		2.81
Adjusted R2	Answer		Jarque-Berra (JB)		Answer
S.E.R	Answer
Observations	75
ANOVA Table
	df	SS	MS	Fobs	Fcritical
Regression	Answer	3473.59		Answer	Answer
Residual	Answer	Answer
Total	74	7698.96
Regression Results
	Coefficients	S.E	t-Stat	P-value	Lower 95%	Upper 95%
Intercept	8.65	1.92	4.51	0.000	4.825	12.475
EDUC	5.28	2.13	2.47	0.016	1.020	9.53
EXPER	3.91	2.46	tobs = Answer	p-val = Answer	-0.995	8.815
TENURE	3.88	1.05	3.68	0.000	CIL = Answer	CIU = Answer

Answer 1