To calculate the coefficient of correlation (often denoted as
Where:
is the number of data points is the independent variable (Price) is the dependent variable (Sales)
Step 1: Calculate the necessary sums
First, let's define our variables based on the given data.
Data: | City | Price (x) | Sales (y) | |----------------|-----------|-----------| | River Falls | 1.30 | 100 | | Hudson | 1.60 | 90 | | Ellsworth | 1.80 | 90 | | Prescott | 2.00 | 40 | | Rock Elm | 2.40 | 38 | | Stillwater | 2.90 | 32 |
Step 2: Calculate the sums
Now, we need to calculate
(the number of cities)
Step 3: Calculate the components
Now let's plug the values into the formula to get
Calculating the numerator:
Calculating the denominator components:
-
First component:
-
Second component:
Now we compute the denominator:
Finally, compute
Conclusion
The coefficient of correlation for the data is approximately