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

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

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

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

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

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 $r$.

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

For the data $(3,14), (5,12), (7,10), (9,8), (11,6), (13,4), (15,2)$, calculate 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 $r$ for the ten pairs: $(1,2), (2,4), (3,5), (4,6), (5,9), (6,10), (7,11), (8,13), (9,14), (10,15)$.

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 $r$.

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

For the set $(1,2), (2,4), (3,6)$ define new variables $x'=2x+3$ and $y'=3y-4$. Show that the Pearson correlation coefficient of $(x',y')$ equals that of $(x,y)$.