A leader of the Workers Union in New Zealand would like to study the movement in the average hourly earnings of New Zealand workers. He collected and recorded data on average earnings (AE, $), labour cost[1] (LC, $) and rate of inflation (RI, %). His data are saved in the t9e3 file.a) Set up a suitable regression model to investigate the impact of labour cost and rate of inflation on the hourly earnings of an average New Zealand worker.b) Do you expect the slope parameters to be positive or negative?c) Estimate the regression model.d) Do the estimated slope coefficients have the logical signs? Carefully explain the meanings of the estimated slope coefficients.e) What do the unadjusted and the adjusted coefficients of determination tell you about the quality of the fit?
Question
A leader of the Workers Union in New Zealand would like to study the movement in the average hourly earnings of New Zealand workers. He collected and recorded data on average earnings (AE, ) and rate of inflation (RI, %). His data are saved in the t9e3 file.a) Set up a suitable regression model to investigate the impact of labour cost and rate of inflation on the hourly earnings of an average New Zealand worker.b) Do you expect the slope parameters to be positive or negative?c) Estimate the regression model.d) Do the estimated slope coefficients have the logical signs? Carefully explain the meanings of the estimated slope coefficients.e) What do the unadjusted and the adjusted coefficients of determination tell you about the quality of the fit?
Solution
a) A suitable regression model to investigate the impact of labour cost and rate of inflation on the hourly earnings of an average New Zealand worker would be a multiple linear regression model. The model could be set up as follows:
AE = β0 + β1LC + β2RI + ε
Where: AE = Average earnings LC = Labour cost RI = Rate of inflation β0 = Y-intercept (average earnings when labour cost and rate of inflation are zero) β1 = Slope coefficient for labour cost (change in average earnings for a one unit change in labour cost) β2 = Slope coefficient for rate of inflation (change in average earnings for a one unit change in rate of inflation) ε = Error term
b) We would generally expect both slope parameters to be positive. An increase in labour cost would likely lead to an increase in average earnings as employers pass on the increased costs to their employees. Similarly, an increase in the rate of inflation would likely lead to an increase in average earnings as employers adjust wages to maintain purchasing power.
c) To estimate the regression model, you would need to use a statistical software package like R, Stata, or SPSS. You would input your data and the software would calculate the estimated coefficients for you.
d) Once you have estimated your model, you would need to look at the signs of your estimated slope coefficients. If they are as expected (positive), this would suggest that your model is correctly specified. The slope coefficients tell you how much average earnings are expected to change for a one unit change in labour cost or rate of inflation, holding all other variables constant.
e) The unadjusted and adjusted coefficients of determination (R-squared and adjusted R-squared) tell you about the goodness of fit of your model. The R-squared tells you the proportion of the variance in average earnings that is explained by your model. The adjusted R-squared adjusts this measure for the number of predictors in your model. If these values are close to 1, this would suggest that your model fits the data well. If they are closer to 0, this would suggest that your model does not fit the data well.
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