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

question 1

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:

Internal Validity

The extent to which a study provides evidence that a causal relationship exists between the variables it examines, free from confounding factors.

Random Assignment

Use of a random "chance" procedure (such as a random number generator or coin toss) to determine the condition in which an individual will participate.

Confounding Variable

A factor other than the independent variable that might produce an effect in an experiment, leading to inaccurate results if not controlled.

Independent Variable

The variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable.