A researcher from the crop and soil sciences department at your local university is interested in the relationship between the amount of phosphorus and nitrogen found in the ground. She takes a random sample of sites in the Commonwealth of Virginia and fits a linear regression model to the data. Based on this model, she obtains the following prediction results:
$$\begin{array} { | c | c | c | c | c | }
\hline \text { Nitrogen Level } & \begin{array} { c }
\text { Predicted } \
\text { Phosphorus Level }
\end{array} & \begin{array} { c }
\text { Std Error } \
\text { Predict }
\end{array} & \mathbf { 9 5 . 0 \% } \text { CI } & \mathbf { 9 5 . 0 \% } \text { PI } \
\hline 20 & 15 & 1.25 & ( 12,18 ) & ( 10,20 ) \
\hline
\end{array}$$ Suppose we wish to predict the phosphorus level of a particular site that had a nitrogen level of 20. What is a 95% interval for the prediction for this site?

Question

A researcher from the crop and soil sciences department at your local university is interested in the relationship between the amount of phosphorus and nitrogen found in the ground. She takes a random sample of sites in the Commonwealth of Virginia and fits a linear regression model to the data. Based on this model, she obtains the following prediction results:
$$\begin{array} { | c | c | c | c | c | } 
\hline \text { Nitrogen Level } & \begin{array} { c } 
\text { Predicted } \
\text { Phosphorus Level }
\end{array} & \begin{array} { c } 
\text { Std Error } \
\text { Predict }
\end{array} & \mathbf { 9 5 . 0 \% } \text { CI } & \mathbf { 9 5 . 0 \% } \text { PI } \
\hline 20 & 15 & 1.25 & ( 12,18 ) & ( 10,20 ) \
\hline
\end{array}$$ Suppose we wish to predict the phosphorus level of a particular site that had a nitrogen level of 20. What is a 95% interval for the prediction for this site?

Quizplus · Accepted Answer

The 95% prediction interval (PI) for the phosphorus level at a site with a nitrogen level of 20 is given as (10, 20), which accounts for the variability in individual predictions.

A Researcher from the Crop and Soil Sciences Department at Your