# Statistical Analysis - Multiple Regression Model

Need assistance interpreting my statistics and ensuring they are correctly performed as well as I need a F Test completed. I've highlighted everything in yellow that I need assistance on. Stats are provided for most questions, just need assistance with interpreting and a F Test

Â© BrainMass Inc. brainmass.com March 5, 2021, 1:49 am ad1c9bdddfhttps://brainmass.com/statistics/correlation-and-regression-analysis/statistical-analysis-multiple-regression-model-625294

#### Solution Preview

Table of Contents

2) Definition of Variables 2

5) Data 3

6) Write the regression equation: 4

6.1 Interpretation????? 4

7) Identify and interpret the t tests for each of the coefficients (one separate paragraph for each variable, in numerical order): 5

7.1 interpret the t tests - Education 5

7.2 interpret the t tests- Gender 6

7.3 interpret the t tests - experience 7

7.4 interpret the t tests - marital 8

7.5 interpret the t tests - children 9

7.6 interpret the t tests - Age 10

8) Identify and interpret the adjusted R2 (one paragraph):< Define "adjusted R2."< 11

What does the value of the adjusted R2 reveal about the model? 62% related, closer than 1 is best.... 11

If the adjusted R2 is low, how has the choice of independent variables created this result? 11

9) Analyze multicollinearity of the independent variables (one paragraph): 12

A) Generate the correlation matrix 12

B) Define multicollinearity 12

C) Are any of the independent variables highly correlated with each other? If so, identify the variables and explain why they are correlated? 12

D) State the implications of multicollinearity (if found) for the model. 12

10) Identify and interpret the F test (one paragraph): 14

A) Using the p-value approach, perform f test 14

B) is the null hypothesis for the F test rejected or not rejected? 14

C) Why or why not? 14

D) Interpret the implications of these findings for the model. 14

â€ƒ

2) Definition of Variables

Y1 Annual Wage - the current annual wage is the dependent variable (DV) in this study. The annual wage is assumed influenced by other factors as outlined in the following independent variables (IV) to follow.

X2 Education -completed years of education

X3 Gender - gender (Female 0, Male 1)

X4 Experience - # of years of work experience

X5 Marital Status - Current marital status (Single 0, Married 1)

X6 Parental Status - Parental status (No Children 0, Children 1)

X7 Age - Age represented in full years

â€ƒ

5) Data

Y1 Wage X2 Education X3 Gender X4 Experience X5 Marital X6 Children X7 Age

$ 17,000.00 8 0 1 1 1 19

22,000.00 12 1 2 0 0 20

27,000.00 12 1 2 0 1 20

20,000.00 12 0 3 0 1 21

44,000.00 12 1 3 0 0 21

48,000.00 13 0 3 1 0 21

20,000.00 12 1 4 1 0 22

36,000.00 18 0 5 0 1 23

30,000.00 16 1 6 0 1 24

28,000.00 12 0 7 0 1 25

47,000.00 16 1 10 0 1 28

50,000.00 16 0 12 1 1 30

65,000.00 16 1 12 1 1 30

75,000.00 18 1 5 1 1 30

70,000.00 16 0 14 1 1 32

42,000.00 13 0 17 0 1 35

61,000.00 14 0 18 1 0 36

80,000.00 17 0 18 1 1 36

100,000.00 18 0 18 1 1 36

37,000.00 18 0 19 1 1 37

33,000.00 12 1 20 1 0 38

32,000.00 14 0 22 1 0 36

38,000.00 12 0 24 0 1 36

50,000.00 11 1 25 0 0 43

34,000.00 17 1 26 1 1 44

30,500.00 16 1 27 1 0 45

50,500.00 12 0 33 1 1 51

85,000.00 11 1 33 0 1 51

45,000.00 12 0 43 0 0 61

32,000.00 12 1 45 0 1 63

38,000.00 16 1 45 1 0 61

49,000.00 12 1 45 1 0 57

55,000.00 16 0 45 1 1 61

145,000.00 18 1 45 1 1 63

$ 40,000.00 14 0 47 0 1 61

6) Write the regression equation:

The regression equation is given as follows:

Wage = -66,521 + 2,649 (Education) + 1,131 (Gender) - 2,350 (Experience) + 8,325 (Marital) + 8,926 (Children) + 3,006 (Age)

6.1 Interpretation?????

Provide a brief definition of each independent variable and how it impacts the equation

X2 Education

X3 Gender

X4 Experience

X5 Marital

X6 Children

X7 Age

The variable 'Education' defines the number of years of education of an individual. The coefficient for the independent variable 'Education' in the given regression model is 2648.63. The positive sign of the coefficient indicates a direct relationship between the dependent and independent variable, i.e., as the number of years of education of an individual increases, the annual wages earned by him also increases. Keeping all other factors constant, as the number of completed years of education increases by 1 year, the annual wages earned is expected to increase by $2648.63.

The variable 'Gender' defines gender of an individual. This variable assumes a value of 0 for female individuals and 1 for male individuals. The coefficient for the independent variable 'Gender' in the given regression model is 1130.50. The positive sign of the coefficient indicates that male individuals (For whom Gender = 1) earn more wages than female individuals (For whom Gender = 0). Keeping all other factors constant, a male individual is expected to earn $1130.50 more as compared to a female individual.

The variable 'Experience' defines the number of years of experience of an individual. The coefficient for the independent variable 'Experience' in the given regression model is -2349.53. The negative sign of the coefficient indicates an inverse relationship between the dependent and independent variable, i.e., as the number of years of experience of an individual increases, the annual wages earned by him decreases and vice versa. Keeping all other factors constant, as the number of years of experience increases by 1 year, the annual wages earned is expected to decrease by $2349.53.

The variable 'Marital' defines marital status of an individual. This variable assumes a value of 0 for unmarried individuals and 1 for married individuals. The coefficient for the independent variable 'Marital' in the given regression model is 8325.38. The positive sign of the coefficient indicates that married individuals (For whom Marital= 1) earn more wages than unmarried individuals (For whom Marital = 0). Keeping all other factors constant, a married individual is expected to earn $8325.38 more as compared to an unmarried individual.

The variable 'Children' defines the parental status of an individual, i.e. whether an individual has children or not. This variable assumes a value of 0 for individuals without children and 1 for individuals who have children. The coefficient for the independent variable 'Children' in the given regression model is ...

#### Solution Summary

The solution comprises of detailed step-by-step analysis of the given multiple regression model.