The variables x x\,x and y y\,y are recorded for 12 items, and the product moment correlation coefficient between x x\,x and y y\,y is -0.47.
The data are then coded using the changes of variable m=log10xm = \log_{10} xm=log10x and n=log10yn = \log_{10} yn=log10y. The product moment correlation coefficient between m m\,m and n n\,n is -0.83, and the regression line of n n\,n on m m\,m is
n=0.25−0.16mn = 0.25 - 0.16mn=0.25−0.16m
Explain how these two correlation coefficients support the use of a model of the form y=axby = ax^{b}y=axb rather than a linear model in x x\,x and yyy.
Show that the relationship between x x\,x and y y\,y can be written in the form y=axby = ax^{b}y=axb, and find the value of a a\,a to 3 significant figures and the value of bbb.
121 exam-style questions on OCR A Level Maths 2.2 Data Presentation and Interpretation, covering 2.2.1 Tables and diagrams for single variable data, 2.2.2 Area in a histogram, 2.2.3 Scatter diagrams and regression lines, 2.2.4 Informal interpretation of correlation, 2.2.5 Correlation and causation, 2.2.6 Measures of average and spread, 2.2.7 Calculations of mean and standard deviation, 2.2.8 Outliers, 2.2.9 Selecting or critiquing data presentation, and 2.2.10 Cleaning data. Each one has a worked solution and a mark scheme showing where the marks go.