A Poultry Farmer That Dabbles in Statistics Is Interested in Exploring

question 33

Essay

A poultry farmer that dabbles in statistics is interested in exploring the relationship between two types of feed (layer pellets and scratch), water, and the output of his laying hens. For ten days he records the number of ounces of layer pellets and scratch the hens consume and the number of fluid ounces of water and tracks the number of eggs that are produced.
$$\begin{array} { | c | c | c | c | } \hline \text { Scratch } & \text { Layer Pellets } & \text { Water } & \text { Eggs } \\\hline 48 & 29 & 36 & 24 \\\hline 44 & 27 & 34 & 22 \\\hline 41 & 22 & 31 & 20 \\\hline 42 & 21 & 32 & 20 \\\hline 48 & 23 & 34 & 22 \\\hline 44 & 28 & 34 & 23 \\\hline 42 & 22 & 37 & 21 \\\hline 41 & 28 & 33 & 22 \\\hline 42 & 22 & 31 & 20 \\\hline 47 & 29 & 37 & 24 \\\hline\end{array}$$ He develops one equation based on three predictors, the scratch, pellets, and water, and another equation based only on the layer pellet consumption. The output for the two models are shown side by side. Comment on the two models and which one should be used.
$$\begin{array} { | l | c | c | } \hline & \text { Pellets, Scratch, Water } & \text { Pellets } \\\hline \text { Multiple R } & 0.994 & 0.904 \\\hline \text { R Square } & 0.987 & 0.817 \\\hline \text { Adjusted R Square } & 0.981 & 0.794 \\\hline \text { Standard Error } & 0.214 & 0.703 \\\hline \text { Observations } & 10 & 10 \\\hline\end{array}$$

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Definitions:

Accounting

The systematic process of recording, summarizing, analyzing, and reporting financial transactions of a business or individual.

Investment

The act of allocating resources, usually capital, with the expectation of generating an income or profit.

Net Income

The profit a company generates after deducting all costs, taxes, expenses, and interest from its total revenue, representing the "bottom line" on an income statement.

Trading Portfolio

A collection of securities held by an institution or individual for the purpose of short-term trading to profit from price changes.