A Poultry Farmer That Dabbles in Statistics Is Interested in Exploring

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.
$$\begin{array} { | l | c | c | } \hline & \text { Pellets, Scratch, Water } & \text { Pellets } \\\hline \text { Multiple R } & 0.994 & 0.904 \\\hline \text { R Square } & 0.987 & 0.817 \\\hline \text { Adjusted R Square } & 0.981 & 0.794 \\\hline \text { Standard Error } & 0.214 & 0.703 \\\hline \text { Observations } & 10 & 10 \\\hline\end{array}$$