For 12 employees, x x\,x is length of service in years and y y\,y is the time in hours taken to complete a task. The correlation coefficient between x x\,x and y y\,y is -0.47. For a one-tailed test of negative association at the 5% significance level, the critical value is -0.4973.
Test at the 5% significance level whether there is evidence of negative association. After the transformations m=log10xm=\log_{10}xm=log10x and n=log10yn=\log_{10}yn=log10y, the correlation coefficient is -0.83 and the fitted line is n=0.25−0.16mn=0.25-0.16mn=0.25−0.16m.
Explain why the transformed model is preferable.
Express y y\,y in the form axbax^baxb, giving a a\,a and b b\,b to 3 significant figures where appropriate.
Use the model to predict y y\,y when x=4x=4x=4. Give your answer to 3 significant figures.