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. After running a multiple regression model, he obtains the following report. What is the best interpretation of these statistics? $$\begin{array} { | l | c | c | c | c | }
\hline & \text { Coefficients } & \text { Std Error } & t \text { Stat } & P \text {-value } \
\hline \text { Intercept } & 1.256 & 1.249 & 1.006 & 0.353 \
\hline \text { Scratch } & 0.185 & 0.032 & 5.714 & 0.001 \
\hline \text { Layer Pellets } & 0.295 & 0.026 & 11.539 & 0.000 \
\hline \text { Water } & 0.149 & 0.041 & 3.587 & 0.012 \
\hline
\end{array}$$
A)For every egg produced, about 0.185 ounces of scratch must be consumed.
B)The standard error for the model intercept is as large as the coefficient, thus the intercept is the most important predictor of egg production.
C)Layer pellets are not good predictors of egg production because the p-value is 0.
D)For every ounce of water consumed, the chickens produce 0.15 eggs, holding all other independent variables constant.

Question

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. After running a multiple regression model, he obtains the following report. What is the best interpretation of these statistics? $$\begin{array} { | l | c | c | c | c | } 
\hline & \text { Coefficients } & \text { Std Error } & t \text { Stat } & P \text {-value } \
\hline \text { Intercept } & 1.256 & 1.249 & 1.006 & 0.353 \
\hline \text { Scratch } & 0.185 & 0.032 & 5.714 & 0.001 \
\hline \text { Layer Pellets } & 0.295 & 0.026 & 11.539 & 0.000 \
\hline \text { Water } & 0.149 & 0.041 & 3.587 & 0.012 \
\hline
\end{array}$$
A)For every egg produced, about 0.185 ounces of scratch must be consumed.
B)The standard error for the model intercept is as large as the coefficient, thus the intercept is the most important predictor of egg production.
C)Layer pellets are not good predictors of egg production because the p-value is 0.
D)For every ounce of water consumed, the chickens produce 0.15 eggs, holding all other independent variables constant.

Quizplus · Accepted Answer

The coefficient for water is 0.149, meaning that for every ounce of water consumed, the number of eggs produced increases by 0.149, holding all other independent variables constant. This is the best interpretation of the statistics given. 
A is incorrect because it refers to the coefficient for scratch, not water. 
B is incorrect because the fact that the standard error for the intercept is as large as the coefficient does not imply that the intercept is the most important predictor. 
C is incorrect because layer pellets are actually good predictors of egg production based on the low p-value.

A Poultry Farmer That Dabbles in Statistics Is Interested in Exploring