Answer:
Correlation between x and y is 0.9508
Step-by-step explanation:
We are given the following in the question:
Distance(x): 1 4 6 6 6 7
Days(y): 2 20 29 38 44 50
We have to find the correlation between x and y.
[tex]\sum y = 183\\\sum x=30\\\bar{x} = \displaystyle\frac{\sum x}{n} = \frac{30}{6} = 5\\\\\bar{y} = \displaystyle\frac{\sum y}{n} = \frac{183}{6} = 30.5\\\\(x-\bar{x}) = -4,-1,+1,+1,+1,+2\\(y-\bar{y}) = -28.5,-10.5,-1.5,7.5,13.5,19.5\\\sum (x-\bar{x}) (y-\bar{y}) = 183\\\sum(x-\bar{x})^2 = 24\\\sum(y-\bar{y})^2= 1543.5\\[/tex]
Formula:
[tex]r = \dfrac{\sum(x-\bar{x})(y - \bar{y})}{\sqrt{\sum(x-\bar{x})^2\sum(y-\bar{y})^2}}[/tex]
Putting values, we get,
[tex]r = \dfrac{183}{\sqrt{24\times 1543.5}} = 0.9508[/tex]
Thus, correlation between x and y is 0.9508
