A scientist is studying the relationship between the concentration of a chemical catalyst, x x\,x units, and the time taken for a reaction to complete, y y\,y seconds.
The scientist records data for 20 different concentrations and finds the product moment correlation coefficient between concentration and reaction time to be -0.35.
Stating your hypotheses clearly and using a 5% level of significance, test whether or not there is evidence of a negative correlation between concentration and reaction time.
The scientist proposes a power model and codes the data using m=log10xm = \log_{10}xm=log10x and n=log10yn = \log_{10}yn=log10y. The regression line is n=2.45−0.72mn = 2.45 - 0.72mn=2.45−0.72m.
The product moment correlation coefficient for the coded data is found to be -0.92.
Explain how this value supports the scientist's proposal.
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.
104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.