Chris is investigating the relationship between the length of time an employee has worked at his company, x x\,x years, and the amount of time it takes them to complete a task, y y\,y hours.
Chris records the time it takes 12 employees to complete the task and finds the product moment correlation coefficient between the length of time the employee has worked at the company and the time taken to complete the task to be -0.47
Stating your hypotheses clearly and using a 5% level of significance, test whether or not the correlation between the length of time an employee has worked the company and the amount of time it takes them to complete the task is negative.
Chris believes that a non-linear model would be a better fit to the data. He codes the data using the coding m=log10xm = \log_{10}xm=log10x and n=log10yn = \log_{10}yn=log10y and obtains the model n=0.25−0.16mn = 0.25 - 0.16mn=0.25−0.16m
The product moment correlation coefficient between m m\,m and n n\,n is found to be -0.83
Explain how this value supports Chris's belief.
Show that the relationship between x x\,x and y y\,y can be written in the form y=axby = ax^by=axb where a a\,a and b b\,b are constants to be found.
