Topic 3 - Linear Regression

Scatterplot

helps us analyze the ASSOCIATION between two quantitative variables

FORM of an association

describes whether a chart is linear or non-linear

DIRECTION of association

describes whether association is positive or negative

STRENGTH of association

how tightly do the points follow the linear trend

correlation coefficient ( r)

unitless measure of the strenght + direction of the linear association between two quantitative variables (value between -1 and 1)

regression line

the best fit line of a scatterplot (that has a linear trend)

outlier points

any data point that is far away from others

leverage points

a data point with an X value that is far away from the average value

influential points

a point that single handedly has a large impact on the slop of the regression model

distinct groups of points

the regression model is not valid if the data contains multiple distinct groups that have different trends

coefficient of determination (R²)

measure of the line of linear regression’s predictive power

interpretation of R²

the percent variation y that can be explained by x

residuals

observed - predicted

negative residual

over-predicted

positive residual

under-predicted

residual plot of a line of regression with a strong coefficient of determination should have

random scatter