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?
Re Statistics
Multiple R 0.993633
R square 0.987307
Adjusted R Square 0.98096
Standard Error 0.213764
observations 10
A) 98.7% of the variability in egg production is explained by the amount of water,
B) The prediction of the amount of eggs is 98.7% accurate based on the amount of
C) The probability that the number of eggs is correctly predicted by the amount of
D) The prediction of the amount of eggs is 99.36% accurate based on the amount of scratch, and layer pellets consumed scratch, layer pellets, and water consumed scratch, layer pellets, and water consumed is 99.36% scratch, layer pellets, and water consumed

Answer 1

Answer:

The correct option is (A).

Explanation:

The R-squared statistic is a measure of the proportion of variability in the dependent variable that is explained by the independent variable(s).

The Multiple R is a statistical measure of the strength of the linear relationship between the deponent variable and the independent variable(s).

The Adjusted R-square is a modified version of R-square. It indicates how well the curve or line fit the data values after adding or removing certain terms from the model. The addition of useless terms in the model decreases the adjusted R-squared value.

The Standard error is an estimate of the standard deviation. The standard error in regression analysis indicates the mean distance the experimental values are from the regression curve or line.

The multiple R value of 0.993633 indicates that there is a perfect positive relationship between the variables.

The R-squared value of 0.987307 indicates that approximately 98.7% of the variability in the number of egg produced is explained by the amount of water.

The adjusted R square value of 0.98096 indicates that the probability of the number of eggs produced, predicted by the amount of water provided is 98%.

Thus, the correct option is (A).