Data Set 6-1
The correlation between the number of PhDs and the number of mules in a state used to be approximately -.90. Accept the following simplified summary data.
$\begin{array}{lll}
& \underline{\text { PhDs}}& \underline{\text { Mules }}\
\text { Mean } & 40 & 200 \
\text { Standard Deviation } & 15 & 50
\end{array}$
In questions based on Data Set 6-1, the task is to predict the number of mules for a state, given the number of PhDs.
-Look at Data Set 6-1. For a state with 60 PhDs the predicted number of mules would be
A) 260
B) 195
C) 140
D) none of the other alternatives are correct.

Question

Data Set 6-1
The correlation between the number of PhDs and the number of mules in a state used to be approximately -.90. Accept the following simplified summary data.
 $\begin{array}{lll}
& \underline{\text { PhDs}}& \underline{\text { Mules }}\
\text { Mean } & 40 & 200 \
\text { Standard Deviation } & 15 & 50
\end{array}$ 
In questions based on Data Set 6-1, the task is to predict the number of mules for a state, given the number of PhDs.
-Look at Data Set 6-1. For a state with 60 PhDs the predicted number of mules would be
A) 260
B) 195
C) 140
D) none of the other alternatives are correct.

Quizplus · Accepted Answer

Using the regression equation $ y = a + bx $, where $ b = r \times \frac{\text{SD of mules}}{\text{SD of PhDs}} $ and $ a = \text{mean of mules} - b \times \text{mean of PhDs} $, we find $ b = -0.9 \times \frac{50}{15} = -3 $. Thus, $ a = 200 - (-3) \times 40 = 320 $. For 60 PhDs, $ y = 320 - 3 \times 60 = 140 $.

Data Set 6-1 the Correlation Between the Number of PhDs

Data Set 6-1
the Correlation Between the Number of PhDs