Answer:
the correlation coefficient of the line of best fit is, 0.98247.
Step-by-step explanation:
Correlation Coefficient are used to find how strong relationship between the data. It expressed its values between +1 and -1. It is represented by r.
* if 0<r<1 indicates a strong positive relationship.
* -1<r <0 indicates a strong negative relationship.
* r=0 indicates no relationship at all.
The formula for this :
[tex]r = \frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}[/tex]
Given the data: (-3, -40) , (1, 12), (5, 72) and (7,137)
Here, n = 4
To calculate the correlation coefficient r;
Substitute the values of data in above formla of r , as shown in the Figure 1:
then;
[tex]r=\frac{4\cdot 1451-(10)(181)}{[4\cdot84-(10)^2][4\cdot 256977 -(181)^2]}[/tex]
or
[tex]r=\frac{5804-1810}{\sqrt{[336-100][102788 -32761]}}=\frac{3994}{\sqrt{[236][70027]}}[/tex]
or
[tex]r=\frac{3994}{4065.26408} =0.98247[/tex]
Therefore, the correlation coefficient r is, 0.98247 (Positive relationship)
