Draw separate scatter diagrams, each with \(8\) points, all in the first quadrant, which represent the situation where the product moment correlation coefficient between variables \(x\) and \(y\) is
\(-1\),
\(0\),
between \(0.5\) and \(0.9\).[3]
An investigation into the effect of a fertiliser on yields of corn found that the amount of fertiliser applied, \(x\), resulted in the average yields of corn, \(y\), given below, where \(x\) and \(y\) are measured in suitable units.
\(x\)
\(0\)
\(40\)
\(80\)
\(120\)
\(160\)
\(200\)
\(y\)
\(70\)
\(104\)
\(118\)
\(119\)
\(126\)
\(129\)
Draw a scatter diagram for these values. State which of the following equations, where \(a\) and \(b\) are positive constants, provides the most accurate model of the relationship between \(x\) and \(y\).
Using the model you chose in part (i), write down the equation for the relationship between \(x\) and \(y\), giving the numerical values of the coefficients. State the product moment correlation coefficient for this model.[3]
Give two reasons why it would be reasonable to use your model to estimate the value of \(y\) when \(x=189\).[2]
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Answer:(a) See example scatter diagrams; (b)(i) D; (ii) \(y=4.18\sqrt x+74.0\), \(r=0.981\); (iii) interpolation and strong transformed correlation.