Question $5$ A study was carried out to determine the influence of a trace element found in soil on the yield of potato plants grown in that soil, defined as the weight of potatoes produced at the end of the season. A large field was divided up into $14$ smaller sections for this experiment. For each section, the experimenter recorded the amount of the trace element found $($in milligrams per metre squared$)$ and the corresponding weight of the potatoes produced $($in kilograms$).$ This information is presented in the worksheet $$Dataset$5$ in the Excel document. Define X as the trace element amount and Y as the yield. Page $51.$ Draw a scatterplot of your data set. $2.$ Calculate the coefficients of a linear equation to predict the yield Y as a function of X$.3.$ Calculate the correlation coefficient for the paired data values. $4.$ Set up the framework for an appropriate statistical test to estab$-$ lish if there is a correlation between the amount of the trace ele$-$ ment and the yield. Explain how having the scatterplot referred to above and having the value of r in advance will influence the structure of your statistical test. $5.$ Carry out and state the conclusion of your test on the correlation. $6.$ Comment on how well the regression equation will perform based on the results above. $3\mathrm{.}9367497$ Additive Yield $78\mathrm{.}19132\mathrm{.}374\mathrm{.}58133\mathrm{.}5878\mathrm{.}98133\mathrm{.}2679133\mathrm{.}9677\mathrm{.}7132\mathrm{.}9573\mathrm{.}69132\mathrm{.}6775\mathrm{.}78133\mathrm{.}371\mathrm{.}57132\mathrm{.}3970\mathrm{.}93133\mathrm{.}4867\mathrm{.}69132\mathrm{.}5464\mathrm{.}07133\mathrm{.}8668\mathrm{.}57132\mathrm{.}6264\mathrm{.}42133\mathrm{.}0964132\mathrm{.}4$