To Investigate the Relationship Between Yield of Potatoes, Y, and Level

question 42

Essay

To investigate the relationship between yield of potatoes, y, and level of fertilizer application, x, a researcher divides a field into eight plots of equal size and applies differing amounts of fertilizer to each. The yield of potatoes (in pounds) and the fertilizer application (in pounds) are recorded for each plot. The data are as follows: $\begin{array}{l|cccccccc}\hline x & 1 & 1.5 & 2 & 2.5 & 3 & 3.5 & 4 & 4.5 \\\hline y & 25 & 31 & 27 & 28 & 36 & 35 & 32 & 34 \\\hline\end{array}$

Summary statistics yield $S S _ { x x } = 10.5 , S S _ { y y } = 112 , S S _ { x y } = 25 , \bar { x } = 2.75$ , and $\bar { y } = 31$ . Find the least squares prediction equation.

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Definitions:

Dividends

Periodic payments made to shareholders, reflecting a portion of a company's profit.

Preferred Shares

A class of ownership in a corporation that has a higher claim on assets and earnings than common shares, often receiving dividends before common shareholders.

Common Stock

A type of equity security that represents ownership in a corporation, entitling the holder to vote on corporate matters and receive dividends.