6 A researcher is investigating various bodily characteristics of frogs of various species. She collects data on length, \(x \mathrm {~mm}\), and head width, \(y \mathrm {~mm}\), of a random sample of 14 frogs of a particular species. A scatter diagram of the data is shown in Fig. 6, together with the equation of the regression line of \(y\) on \(x\) and also the value of \(r ^ { 2 }\).
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\includegraphics[alt={},max width=\textwidth]{e3ac0ba0-9692-4018-894e-2b04b07eaf32-6_949_1616_450_228}
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\caption{Fig. 6}
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- (A) Use the equation of the regression line to estimate the mean head width for frogs of each of the following lengths.
- 45 mm
- 60 mm
(B) Comment briefly on each of the estimates in part (i)(A). - Explain how the mean length of frogs with head width 16 mm should be estimated.
- Calculate the value of the product moment correlation coefficient.
- In the light of the information in the scatter diagram, comment on the goodness of fit of the regression line.