Answer:
a. 0.83
b. 44107.3
c. 2252.7
Step-by-step explanation:
a)
The correlation coefficient is calculated as
byx=rSy/Sx
rSy=byx*Sx
⇒r=byx*Sx/Sy
Sy=standard deviation of y=standard deviation of current salary=15300
Sx=standard deviation of x=standard deviation of beginning salary=5970
byx=2.12
r=2.12*5970/15300
r=12656.4/15300
r=0.83
There is a strong positive correlation between current and beginning salary.
b)
Beginning salary=$22000
As
y^ =−2532.7 + 2.12x.
Current salary=-2532.7+2.12*beginning salary
Current salary=-2532.7+2.12*22000
Current salary=-2532.7+46640
Current salary=$44107.3
The predicted current salary of Mr. Joseph Keller is $44107.3.
c)
Residual=y-y^=Observed-Predicted
Observed Current Salary of Kathy Jones=40000
Beginning salary of Kathy Jones=19000
y^ =−2532.7 + 2.12x.
Predicted Current salary=-2532.7+2.12*beginning salary
Predicted Current salary=-2532.7+2.12*19000
Predicted Current salary=-2532.7+40280
Predicted Current salary=$37747.3
Residual=Observed Current Salary-Predicted Current salary
Residual=40000-27747.3
Residual=$2252.7
The residual for Ms. Jones is $2252.7.
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