Question

QUESTION-1: (50 P) A pharmaceutical company wants to model the relationship between the salaries of research scientists with their gender, years of experience, and an index of publication quality. Table below is a random sample from company's records. S/N Salary Gender Publication Years 1 88,0 F 4,5 11 2 77,3 M 7,8 6 Female Gender = Cols Male . 35 87,7 M 5,1 8 a) MS Excel output for multiple regression model including interaction terms of gender and other variables given below. Fill in the blank cells of the table (16 cells with question marks). SUMMARY OUTPUT Regression Statistics Multiple R 0,950 R Square ? Adjusted R Square ? Standard Error 2 Observations 35 ANOVA df ? ? ? SS 5517,69 ? 6108,63 Regression Residual Total MS 1103,54 ? F ? Significance F 7.97 E-14 1

Answer 1

We have given incomplete output of the multiple regression :

## a) complete tables :

Summary statistics : Regression statistics :

Multiple R	0.950
R Square	0.9025
Adjusted R square	0.8857
Standard error	4.5141
Observation	35

ANOVA :

Source	df	SS	MS	F	Sig F value
Regression	5	5517.69	1103.538	54.1555	7.97E - 14
Error	29	590.94	20.3772
Total	34	6108.63

# Degree of freedom for regression : SS regression / MS regression

= 5517.69 / 1103.538 = 4.9999 ie 5

## Degree of freedom for total = n -1 here n = total observation is equal to 35

hence degree of freedom for total = 34

# Degree of freedom for Error = Df total - Df regression = 34 - 5 = 29

## SS error = SS total - SS regression = 6108.63 - 5517.69 = 590.94

## MS error = SS error / df error  

= 590.94 / 29

= 20.3772

## F statistics : MS regression / MS error = 1103.538 / 20.3772

= 54.1555

## R square = r² where r = correlation coefficient of multiple R

R square = ( 0.950 ) ² = 0.9025

Adjusted R square = 1 - [ ( 1 - R square ) * ( ( n -1 ) / ( n - ( k + 1))

here k = 5

Adjusted R square = 1 - [ ( 1 - 0.9025 ) * ( 34 / 29 ) ]

= 1 - 0.1143

= 0.8857

# Standard error = SQRT ( MS error )

= 4.5141

## Test for regression model :

To test :

Ho : overall regression model is not significant VS

H1 : overall regression model is significant

Test statistics : F = 54 .1555

p value = 0.000

α = 0.05

Decision :

we reject Ho if p value is less than  α value using p value approach here p value is less than  α

value here we reject Ho at given level of significance .

Conclusion :

There is sufficient evidence to conclude that overall regression model is significant at given

level of significance .