Question Type 1: Calculating the Pearsons moment-correlation coefficient r for a bivariate data set Exercises

Calculate the Pearson correlation coefficient $r$ for the bivariate data set: $(1,2), (2,4), (3,6)$.

Calculate the Pearson correlation coefficient $r$ for the data: $(1,8), (2,6), (3,4), (4,2)$.

Given $n=6$, $\sum x=36$, $\sum y=52$, $\sum x^2=260$, $\sum y^2=500$, $\sum xy=270$, compute the Pearson correlation coefficient $r$.

Find the Pearson correlation coefficient for the data points $(2,1), (4,3), (6,5), (8,7), (10,9)$.

For the data $(3,14), (5,12), (7,10), (9,8), (11,6), (13,4), (15,2)$, calculate the Pearson correlation coefficient $r$.

Calculate the Pearson correlation coefficient $r$ for the data: $(1,3), (2,5), (3,7), (4,9)$.

Given that $\sum (x-5)(y-4)=50$, $\sum (x-5)^2=100$, $\sum (y-4)^2=80$, find the Pearson correlation coefficient $r$.

Given $n=5$, $\sum x = 15$, $\sum y = 20$, $\sum x^2 = 55$, $\sum y^2 = 98$, $\sum xy = 67$, compute the Pearson correlation coefficient $r$.

The marks of 6 students in Maths ($x$) and Physics ($y$) are: $x=(45, 50, 55, 60, 65, 70)$, $y=(78, 82, 85, 88, 90, 93)$. Calculate the Pearson correlation coefficient $r$.

Calculate the Pearson correlation coefficient for: $x=(100, 150, 200, 250, 300)$ $y=(20, 45, 70, 95, 120)$

Consider the set of points $(1, 2)$, $(2, 4)$ and $(3, 6)$. Define new variables $x' = 2x + 3$ and $y' = 3y - 4$.

Show that the Pearson correlation coefficient of $(x', y')$ equals that of $(x, y)$.

Calculate the Pearson correlation coefficient $r$ for the ten pairs: $(1,2), (2,4), (3,5), (4,6), (5,9), (6,10), (7,11), (8,13), (9,14), (10,15)$.