A collector tracks the value of a vintage guitar over 10 years. The time, xxx (years), and the value, yyy (in £1000s), are recorded in the table below.
| xxx | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| yyy | 8.5 | 10.2 | 12.8 | 15.5 | 18.9 | 23.1 | 28.4 | 34.2 | 41.5 | 50.8 |
The data is coded using the changes of variable r=xr = xr=x and s=log10ys = \log_{10} ys=log10y.
The product moment correlation coefficient for the coded data is 0.97. Comment on r r\,r for this model and therefore justify the use of a model in the form y=abxy = ab^xy=abx where a a\,a and b b\,b are constants.
The regression line of s s\,s on r r\,r is found to be s=0.840+0.086rs = 0.840 + 0.086rs=0.840+0.086r.
Find the values of a a\,a and bbb, give your answers to 3 significant figures.
