1.1. An owner of a beach resort is comparing parasol sales, £p, and sun cream sales, £s, at the resort over a period of eleven days. The data is standardised by coding the variables using x = $\frac{s-153}{103}$ and  y = $\frac{p-32}{37}$. The values for the first ten days are plotted on the scatter diagram below.

(i) On the eleventh day, the resort sold £246 worth of sun cream and £69 worth of parasols. Use this information to complete the scatter diagram. 

(ii) The equation for the regression line of y on x is  y = 0.19+0.83x.  Add the regression line to the scatter diagram.

1.2. (i) Show that by using the regression line of y on x and the coding equations above, the regression line of p on s can be written in the form  p = a + bs,  where a and b are constants to be found to 3 significant figures. 

(ii) Hence, or otherwise, find an estimate for the amount of parasol sales on a day where there are £170 of sun cream sales.