Peter owns the Newcastle Arms Pub. Peter believes that sales of ice-filtered cider in the pub are linked to the average monthly temperature, with higher sales being recorded in months with higher temperatures. To investigate, Peter records the average monthly temperature in the local town over a period of one year ($X$ degrees Celsius), along with total monthly sales of ice-filtered cider ($Y$ hundred pounds). The results are shown in the table below:
| Month |
$\var{obj[0]}$ |
$\var{obj[1]}$ |
$\var{obj[2]}$ |
$\var{obj[3]}$ |
$\var{obj[4]}$ |
$\var{obj[5]}$ |
$\var{obj[6]}$ |
$\var{obj[7]}$ |
$\var{obj[8]}$ |
$\var{obj[9]}$ |
$\var{obj[10]}$ |
$\var{obj[11]}$ |
| $X$ (temperature) |
$\var{r1[0]}$ |
$\var{r1[1]}$ |
$\var{r1[2]}$ |
$\var{r1[3]}$ |
$\var{r1[4]}$ |
$\var{r1[5]}$ |
$\var{r1[6]}$ |
$\var{r1[7]}$ |
$\var{r1[8]}$ |
$\var{r1[9]}$ |
$\var{r1[10]}$ |
$\var{r1[11]}$ |
| $Y$ (sales, £100s) |
$\var{r2[0]}$ |
$\var{r2[1]}$ |
$\var{r2[2]}$ |
$\var{r2[3]}$ |
$\var{r2[4]}$ |
$\var{r2[5]}$ |
$\var{r2[6]}$ |
$\var{r2[7]}$ |
$\var{r2[8]}$ |
$\var{r2[9]}$ |
$\var{r2[10]}$ |
$\var{r2[11]}$ |
You are given the following information:
| $X$ |
$\sum x=\;\var{t[0]}$ |
$\sum x^2=\;\var{ssq[0]}$ |
| $Y$ |
$\sum y=\;\var{t[1]}$ |
$\sum y^2=\;\var{ssq[1]}$ |
Also you are given $\sum xy = \var{sxy}$.