A logistics manager is studying the relationship between the age of a delivery van, x x\,x years, and its current resale value, y y\,y thousands of pounds.
She records the data for 10 vans and calculates the product moment correlation coefficient between the age and the resale value to be -0.51.
Stating your hypotheses clearly and using a 5% level of significance, test whether or not there is evidence of a negative correlation between the age of a van and its resale value.
The manager decides to test a non-linear model. She codes the data using m=log10xm = \log_{10}xm=log10x and n=log10yn = \log_{10}yn=log10y and finds the regression line to be n=1.35−0.48mn = 1.35 - 0.48mn=1.35−0.48m.
The product moment correlation coefficient between m m\,m and n n\,n is calculated as -0.94.
Explain how this value supports the use of a non-linear model.
Show that the relationship between x x\,x and y y\,y can be expressed in the form y=axby = ax^by=axb, where a a\,a and b b\,b are constants to be determined.
