# Linear Regression and Correlation

Question 1. Refer to the Wage Data which reports information on annual wages for a sample of 100 workers. Also included are variables relating to the industry, years of education, and gender for each worker. Wage Data is at: http://highered.mcgraw-hill.com/sites/0073030228/student_view0/index.html

a. Determine the correlation between the annual wage and the years of education. At the .05 significance level can we conclude there is a positive correlation between the two variables?

b. Determine the correlation between the annual wage and the years of work experience at the .05 significance level can we conclude there is a positive correlation between the two variables?

Question 2: Refer to the CIA data which reports demographic and economic information on 46 countries at: http://highered.mcgraw-hill.com/sites/0073030228/student_view0/index.html

a. You wish to use the labor force variable as the independent variable to predict the unemployment rate. Interpret the slope value. Use the appropriate linear regression equation to predict unemployment in the United Arab Emirates.

b. Find the correlation coefficient between the levels of exports and imports. Use the .05 significance level to test whether there is a positive correlation between these two variables

c. Does there appear to be a relationship between the percentage of the population over 65 and the literacy percentage? Support your answer with statistical evidence. Conduct an appropriate test of hypothesis and interpret the results.

PS: Any tips/pointers you can give for how to go about interpreting the regression equation, the coefficient, the interval, correlation, slope values etc--when it comes to linear Regression & Correlation so it's easier for me to understand?say in pointer form? Thanks

#### Solution Preview

For an overview of correlation and regression, look at the last problem first.

a. Determine the correlation between the annual wage and the years of education. At the .05 significance level can we conclude there is a positive correlation between the two variables?

The correlation coefficient is r. To find it in Excel, use the function PEARSON().

r = 0.408

The correlation coefficient is positive, which means that more education is associated with higher wages.

To see if it is significant, use a table to look up the critical value of r (with the correct degrees of freedom (df = n - 2 = 98); http://www.gifted.uconn.edu/siegle/research/Correlation/corrchrt.htm) or use a calculator like this: http://secamlocal.ex.ac.uk/people/staff/dbs202/cat/stats/corr.html.

Our value of r is greater than the critical value of r = 0.195. Therefore, the correlation is significantly different from 0 at the 0.05 level.

b. Determine the correlation between the ...