You’ve probably heard that earnings are generally higher in urban areas than in rural areas. But why is this so? Perhaps it’s because urban areas attract a cluster of employers, producing any employment opportunities. To test this possibility, Statistics Canada used census data to run a multivariate regression of weekly earnings (w) in a given location against employment in the same location (EL) and employment in the same location and the same industry (ELI). Preliminary data analysis had shown that these variables are nonlinearly related, so natural logarithms (ln) were taken before running the regression. The result was

ln (w) = 5.85 + 0.035 × ln (EL) + 0.009 × ln (ELI).

The P-values associated with the intercept and the two coefficients in the above equation are ,0.001, ,0.001, and 0.117. The F-ratio has a P-value 0.001.

a) Is the regression model significant overall?

b) Which variable(s) is (are) significantly related to weekly earnings at the 95% level? What form does this relation take, linear or other (specify)?

c) Suppose there was a 3% increase in EL in Oshawa, Ontario, but ELI remained constant. By what percentage would you expect weekly earnings to increase in Oshawa?

d) Does this regression show that education level is not linearly related to weekly earnings?