3.1 - Scatterplots & Correlation

Scatterplots

A graphial representation of two variables, that allows us to determine any relationshop that may exist between two. They have two axes, each measuring the values of one varaible:

• The vertical axis or Y-axis

• The horizontal axis or X-axis

Scatterplot + Quadrants

I : both above their mean

II : X below the mean, Y above the mean

III : both above their mean

IV : X above mean, Y below mean

More of X comes with more Y: Positive relationship

Correlation Coefficent

summerizes the direction and strength of the linear association between two variables

A correlation between 0 and 1 means

a positive linear relationship

A correlation of 1 means

a perfect positive linear relationship

A correlation between −1 and 0

means a negative linear relationship

A correlation of −1 means

a perfect negative linear relationship

A correlation of 0 means

that there is no linear relationship

The further from 0

the stronger the correlation

z-scores

• represents the number of standard deviations that the observation is above or below the mean of variable

• how far an observation is from the average, relative to how much variation a particular variable has

• Xi - (average of) X tells us how much Xi, is above or below the mean of X (average of) X

• When dividing by the standard deviation of X, it tells us how many standard deviations it is above or below the mean