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.
