1. 9.1B – Computing the Correlation Coefficient by Hand
Correlation coefficient = strength and direction of a linear relationship between variables graphed in a scatter plot.
r = n∑xy – (∑x)(∑y)
n∑x² - (∑x)² n∑y² - (∑y)²
n= # of data points
Make a table to compute this!!!

2. Steps to calculating r 1) Find the Sum of the x- values: ∑x
2) Find the Sum of the y-values: ∑y
3) Multiply each x by corresponding y and find the sum: ∑xy
4) Square each x-value and find the Sum: ∑x²
5) Square each y-value and find the Sum: ∑y²
6) use these 5 sums in the formula for r
r = n∑xy – (∑x)(∑y)
n∑x² - (∑x)² n∑y² - (∑y)² n=# points

3. Calculate r with calc. & by Hand
X Y X Y XY X² Y²
2.4
225
1.6
184 2
220
2.6
240
1.4
180
186
2.2
215
∑X=
∑Y=
∑XY=
∑X²=
∑Y²=

4. Computing r ∑X= 15.8 ∑Y= 1634 ∑XY= 3289.8 ∑X²=32.44 ∑Y²=337,558
r = n∑xy – (∑x)(∑y)
n∑x² - (∑x)² n∑y² - (∑y)²
8(3289.8) – (15.8)(1634)
8(32.44) – 15.8² 8(337,558) ²
501.2
( ,508 )
r≈ 0.913