6. Penshop have stores selling stationary in each of 6 towns. The population, \(P\), in tens of thousands and the monthly turnover, \(T\), in thousands of pounds for each of the shops are as recorded below.

1. Represent these data on a scatter diagram with \(T\) on the verical axis.
2. 1. Which town's shop might appear to be underachieving given the populations of the towns?
   2. Suggest two other factors that might affect each shop's turnover. You may assume that $$\Sigma P = 37.9 , \quad \Sigma T = 85.8 , \quad \Sigma P ^ { 2 } = 264.69 , \quad \Sigma T ^ { 2 } = 1286 , \quad \Sigma P T = 574.25 .$$
3. Find the equation of the regression line of \(T\) on \(P\).
4. Estimate the monthly turnover that might be expected if a shop were opened in Gratton, a town with a population of 68000.
5. Why might the management of Penshop be reluctant to use the regression line to estimate the monthly turnover they could expect if a shop were opened in Haggin, a town with a population of 172000 ?