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
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 -0.91
Explain how this value supports Chris's belief.
340 exam-style questions on Edexcel A Level Maths Regression, Correlation and Hypothesis Testing, covering 1.1 Exponential Models, 1.2 Measuring Correlation, and 1.3 Hypothesis Testing for Zero Correlation. Each one has a worked solution and a mark scheme showing where the marks go.