5. As a statistical consultant, you have been asked to develop a linear model which shall be given to first year executive MBA students.

VariableNameDescription

X1CountryU.S. or International Student

X2Work ExperienceYears of Work Experience

X3Work BackgroundMarketing, Financial, IT, Human Resources

YIncomeAnnual Income in Thousands of Dollars

Assume that you will have many observations for this model.However, here are just the first four observations of this data set:

CountryWork ExperienceWork BackgroundIncome (thousands $)

U.S.5 yearsMarketing$75

International2 yearsFinancial$70

International8 yearsIT$95

U.S.3 yearsHuman Resources$80

A.Further assume that your junior research partner, who has never taken STA-580, and was asked to conduct the survey and has given their matrix design resulting from the survey.

X= 1 5 1

2 2 2

2 8 3

1 3 4

Y =7500

70

95

80

B= B1

B2

B3

A. Where for Country, we have1=U.S. , 2= Internation al.For Work Background, we have 1 = Marketing, 2=Financial, 3= IT, and 4= Human Resources for the 3^rdcolumn of X.

Please comment on the appropriateness of your junior research partner's attempt at creating a Design, Response, and Parameter Matrix.What mistakes were made?

B.Now, Find an alternate design matrix [X], parameter matrix [B], and the general regression equation (algebraically) for this survey that is correctly done.Do it for just the first 4 observations you see in the data set. The objective here is to only determine only if the predictors are significant predictors of income.No other predictors, higher order terms, or interaction terms are necessary.