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Computer Assignment 2

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User Generated

Subject

Statistics

Type

Homework

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oelnar7200

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Estimated Regression Equation

Annual Income (Y) = -15.1351607 + 0.674189248 Age (X1) + 1.854227224 Years of Education

(X2) - 0.04284961 Years of Work (X3)

Prediction of Annual Income

For the given age of 37 years, 12 years of education, and 10 years of work of an adult, the

estimated annual income is 31.63207 (in thousands).

Annual Income (Y) = -15.1351607 + 0.674189248 Age (X1) + 1.854227224 Years of Education

(X2) - 0.04284961 Years of Work (X3)

= -15.1351607 + (0.674189248*37) + (1.854227224 *12) – (0.04284961*10)

= 31.63207 (000)

Overall Significance of the Regression Relationship

Overall significance of the regression relationship is assessed with F test. More specifically, how

all the independent variables as a whole affect the dependent variable can be understood from

the F test result. The p value of the F test is 0.000105436. This p value represents the lower

level of significance for which null hypothesis is rejected. Here is p value of the F test is lower

than the level of significance (0.05) of the test. As the significance level of the F value is lower

than the level of significance null hypothesis can be rejected. Thus, conclusion can be drawn

that the model as a whole is statistically significant. More specifically, all the independent

variables including age, years of education, and years of work in combined has statistically

significant relationship with the annual income of a person.

Impact of Age and Years of Education on Annual Income

The regression n coefficient of Age and Years of Education are 0.674189248, and 1.854227224

respectively. Here the sign of the regression coefficient of Years of Education and Age are

positive. From the sign of the regression coefficient of age it is implied that if the age of a person

increases by 1 year, the income of that person will increase by 0.674189248 (in thousands), and

if the year of education of a person increases by 1 year, the income of that person will increase

by 1.854227224 (in thousands). The regression coefficient of Years of Education and Age in the

regression model are found statistically significant as implied from the lower value of p value of

age (0.03976113), and Years of education (0.00142553) than the level of significance (0.05).

Thus, it can be said that there exists a true (statistically significant) relationship of Age and

Years of Education with the annual income.

Regression Coefficient Table

Coefficients

Standard Error

t Stat

P-value

Intercept

-15.1351607

7.788238329

-1.9433356

0.07799758

Age (X1)

0.674189248

0.289160726

2.3315381

0.03976113

Years of Education (X2)

1.854227224

0.438921682

4.2245059

0.00142553

Years of Work (X3)

-0.04284961

0.482485598

-0.0888101

0.9308291

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Estimated Regression Equation Annual Income (Y) = -15.1351607 + 0.674189248 Age (X1) + 1.854227224 Years of Education (X2) - 0.04284961 Years of Work (X3) Prediction of Annual Income For the given age of 37 years, 12 years of education, and 10 years of work of an adult, the estimated annual income is 31.63207 (in thousands). Annual Income (Y) = -15.1351607 + 0.674189248 Age (X1) + 1.854227224 Years of Education (X2) - 0.04284961 Years of Work (X3) = -15.1351607 + (0.674189248*37) + (1.854227224 *12) – (0.04284961*10) = 31.63207 (000) Overall Significance of the Regression Relationship Overall significance of the regression relationship is assessed with F test. More specifically, how all the independent variables as a whole affect the dependent variable can be understood from the F test result. The p value of the F test is 0.000105436. This p value represents the lower level of signific ...
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