Question

A social scientist would Ilike to analyze the relationship between educational attainment and salary. He collects a sample data, where "Education" refers to years of higher education and "Salary" is the individual's salary in thousands of dollars. The summary statistics are as follow:

EDUCATION MEAN 4 ST DEV 2.45

SALARY MEAN 60.34 ST DEV 24

  

mean	st dev
4	2.45
60.34	24.95

According to the data, the correlation coefficient between "Education" and "Salary" is 0.9212

a. Find a linear equation to predict the "Salary" from the "Education"

b. Find the coefficient of determination and explain the meaning of it.

C. Suppose an individual has completed 7 years education, predict his salary based on the linear regression model.

d. Interpret the slope and intercept of the regression line

Answer 1

Explanatory variable(X) - education and dependent variable(Y) - salary

The value of estimated slope

The value of estimated y intercept

a) The estimated linear regression equation is :

Salary = 22.8152 + 9.38120*Education

b) The coefficient of determination R² = 0.9212²= 0.8486

84.86% variation in salary can be explained by the above regression equation using education as predictor.

c) The predicted salary for an individual with  7 years education = (22.8152 + 9.38120*7) K = 88483.6 dollars

d) Interpretation of the slope : For a number of years of education increase, predicted salary will increase 9.38120 thousand dollars.

Interpretation of the intercept : When number of years of education = 0, predicted salary = 60.34 thousand dollars.