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.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.