Answer
a. The scatter diagram can be constructed by hand or using a software.
b. the value of r is 0.816286739. This is evidence that there exists a correlation between x and y.
c. The outlier.
Work Step by Step
Step 1
We calculate the linear correlation coefficient which will help us to make a decision on whether there is a linear correlation or not.
We use the formula:
$r= \frac{n(∑xy)-(∑x)(∑y)} {\sqrt{n(∑x^2 )-(∑x)^2 } \sqrt{n(∑y^2 )-(∑y)^2 }} $
Step 2
We find the statistics as follows:
$∑x=99$
$∑y=82.5$
$∑xy=797.47$
$∑x^2 =1001$
$∑y^2 =659.9762$
Step 3
Replace the statistics in the formula with their respective values.
$r= \frac{(11*797.47)-(99)(82.5)} {\sqrt{11(1001)-99^2 } \sqrt{11(659.976)-82.5^2 }}$
Step 4
The value of r is
$r=0.816286739$
Step 5
We conclude that there is a linear correlation between x and y since the value of r is closer to 1.
