A regression analysis was conducted to examine the factors influencing income (m

Question

A regression analysis was conducted to examine the factors influencing income (measured in thousands of dollars). The model contains a variable for age (in years), years of education, a categorical variable for sex (women=1; men are the reference category), and a categorical variable for race (dummy variables are used for White and Black; All Other Races are the reference category). The results from the regression analysis are below:

                            Estimate     Standard Error           T-Value                 P-Value

Intercept                3.60                   0.80                        7.00                    < 0.0005

Age                         0.09                    0.02                       3.00                       0.003

Education              2.06                    0.90                       2.40                       0.008

Female                  -3.67                   1.42                       -2.24                      0.013

White                    4.33                    2.13                         1.99                         0.047

Black                   -0.83                    0.47                         1.88                         0.060

                            Value                   df                            P-Value

F(obtained)        78.567                (995, 5)                     < 0.0017

R2                        0.372

The mean for each independent variable is:

Age (Years)

38.50

Education (Years)

11.20

Female

0.62

White

0.48

Black

0.25

Use the information from the table to answer the questions below. Please keep

your answers brief –you do not need to write a lot to answer these questions.

e) Pick one interval-ratio variable and interpret the partial slope. (10 points)

f) Pick one dummy variable and interpret the partial slope. (10 points)

g) Complete the table to indicate whether each of the partial slopes is statistically

significant at 95% confidence. (5 points)

Variable

Significant?

Intercept

Yes

Age (Years)

Education (Years)

Female

White

Black

h) What is the predicted value for a Black male (other values held constant at their means)? Show your work. (10 points)

Age (Years)

38.50

Education (Years)

11.20

Female

0.62

White

0.48

Black

0.25

Explanation / Answer

e) Pick one interval-ratio variable and interpret the partial slope.

Answer : Here i have picked age as interval ratio varaible and its partial slope is equal to 0.09. That means if we keep all the other variables constant, then by increasing one unit (one year ) of age will increase 0.09 unit (thousand dollars) in income.

(f) Pick one dummy variable and interpret the partial slope.

Answer : Here i pick the dummy variable SEX (Here for women = 1 , men = 0) so here the slope coefficient = -3.67. Here we can interpret that an women earn -3.67 units (in thousand) less income than their male counterpart if all other variables are kept constant.

(g) Complete the table to indicate whether each of the partial slopes is statistically significant at 95% confidence.

Answer :

Here for black, the p - vlaue is greater than 0.05 so the variable is not significant.

(h) What is the predicted value for a Black male (other values held constant at their means)? Show your work.

Answer :

Age = 38.50 year , Education = 11.20 years , White = 0 , black = 1 , Female = 0

Here the regression model is

Earnings = 3.60 + 0.09 * age + 2.06 * Education -3.67 * female + 4.33 * white - 0.83 * Black

Earnings = 3.60 + 0.08 * 38.50 + 2.06 * 11.20 - 3.67 * 0 + 4.33 * 0 - 0.83 * 1 = 28.922 thousan dollars

Variables P - value Significant Age 0.003 Yes Education 0.008 Yes Female 0.013 Yes White 0.047 Yes Black 0.06 NO

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