An outlier reverses the fitted trend

A chemical is sprayed onto various plots of land. After a year the concentration, $x$, of the chemical is measured in each plot, and also the concentration, $y$, of bacteria in the plot. Both $x$ and $y$ are measured in appropriate units. A statistician is given the following data to analyse.

$x$	5.11	6.17	4.71	4.15	3.87	2.72	10.13	5.44
$y$	4.23	3.98	4.81	6.30	7.82	9.45	11.71	4.15

(i) Calculate the correlation coefficient, and the line of regression of $y$ on $x$.3 marks

(ii) Give a sketch of the scatter diagram for the data, as shown on your calculator. Giving a reason, identify a data pair which should be regarded as suspect.3 marks

(iii) Remove the suspect data pair, and calculate the correlation coefficient, and the line of regression of $y$ on $x$, for the revised data.2 marks

(iv) Comment of your answers to part (i) and (iii).2 marks

Two other plots of land, A and B, are to be sprayed with the chemical. The value of $x$ for A is to be 1.2 and the value of $x$ for B is to be 4.95.

For each of these two plots, find the estimated value of $y$, using the line of regression obtained in part (iii), and state, with a reason in each case, whether it would be good practice to regard this value as a valid prediction.4 marks