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.

Additive Yield

$74106\mathrm{.}93$

$70\mathrm{.}92107$

$67\mathrm{.}98108\mathrm{.}14$

$71\mathrm{.}34108\mathrm{.}32$

$67\mathrm{.}7108\mathrm{.}43$

$64\mathrm{.}12108\mathrm{.}31$

$60\mathrm{.}62109\mathrm{.}33$

$61\mathrm{.}79107\mathrm{.}81$

$59109\mathrm{.}87$

$60\mathrm{.}13109\mathrm{.}52$

$59\mathrm{.}44111\mathrm{.}07$

$61\mathrm{.}17109\mathrm{.}35$

$65\mathrm{.}13107\mathrm{.}1$

$66\mathrm{.}03107\mathrm{.}65$

Draw a scatterplot of your data set.

Calculate the coefficients of a linear equation to predict the yield Y as a function of X$.$

Calculate the correlation coefficient for the paired data values.

Set up the framework for an appropriate statistical test to establish if there is a correlation between the amount of the trace element 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.

Carry out and state the conclusion of your test on the correlation.

Comment on how well the regression equation will perform based on the results above. can you answer each part of question with all steps and calcuation please asap