Question

Following Question 1. The researcher thought that another variable, gender, might also affect the income level. Thus, he created a dummy variable for gender (1 for male and 0 for female) and estimated the regression model with two independent variables.

a) Write down the estimated regression equation.

b) What is the value of R square in this regression model? Compared with the R-square in Question 1, what is the additional contribution of gender to the percentage of variance explained?

c) Interpret the meaning of the regression coefficient of Year in College (how does year in college affect salary?). Does this variable have a significant impact on income level at α= .05? How does one more year in college affect salary if the gender is the same? How do you get this conclusion?

d) Explain the meaning of the coefficient of gender (how does gender affect salary?). Does this variable have a significant impact on income level at α= .05? How do you get this conclusion?

e) If a female salesperson told you that she has a 2-year college degree, what is your prediction on her annual income?

Answer 1

By using the given output

salary = y

a)

The estimated regression equaation

= 4.667 + 7.604 years in college + 4.402 gender

b)

The value of R2 in this regression model is 0.971

97.1% of the variation in salary can be explained by the regression model.

c)

Interpretation:

For each additional increase of 1 year in college , the salary increase by $7.604 , holding gender remains constant.

The value of the test statistics t = 15.165

Conclusion:

t > tcritical , then reject the null hypothesis, year in college has a significant impact on income level.

Now,

For each additional increase of 1 male , the salary increase by $4.042 , holding year in college remains constant.

The value of the test statistics t = 4.030

Conclusion:

t > tcritical , then reject the null hypothesis, Gender has a significant impact on income level.

d)

Interpretation:

If we consider gender as male then it will increase salary on an average by 4.042 if we keep Years in College zero.

Since the p-value for Gender= 0.005 < 0.05 level of significance so we conclude that Gender is significant variable.

e)

From given information

Annual Income = 4.667+7.604 Years in College +4.042 gender

Years in College = 2 , female = 0

Annual Income = 4.667+7.604*2 + 4.042*0

Annual Income = 19.875

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