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!!!

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

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

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) - 1634² 501.2 ( 9.88 30,508 ) r≈ 0.913