91Ó°ÊÓ

Whether the use of linear correlation coefficient is appropriate or not.

The data of twenty samples of varying fibre-density were each counted by $10$viewers by means of an eyepiece method and a television-screen method.

$\begin{array}{|ll|}\hline \text{EYE PIECE}& \text{TV}\\ 3.5& 1.8\\ 4.5& 7.4\\ 8.8& 3.2\\ 7.9& 5.8\\ 8.3& 11.5\\ 13.8& 5.6\\ \hline\end{array}$

$\begin{array}{|ll|}\hline 18.3& 23.9\\ 20.8& 46.8\\ 23.1& 21.7\\ 49.5& 84.6\\ 86.3& 55.4\\ 89.2& 115.8\\ 105.1& 92.4\\ \hline\end{array}$

$\begin{array}{|ll|}\hline 116.1& 182.4\\ 145.2& 135.7\\ 201.5& 281.4\\ 224.8& 89.6\\ 250.5& 194.7\\ 285& 300.4\\ 307.9& 314.9\\ \hline\end{array}$

The scatterplot for the given data can be drawn by using the MINITAB:

From the above scatterplot, it is not reasonable to find a regression line for the data because the observations regarding Eye Piece method and TV screen methods forms a quadratic pattern. Hence, there is no linear pattern visible in the given data. Therefore, the parts (b) - (c) will be omitted.