Scatterplots Regression, Residuals

Scatterplots Used to show relationships between two variables Used to illustrate trends over time (time series data)

Looking for Trends Scatterplots can exhibit various trends: Steady growth / decline Irregular growth / decline

Regression The process of fitting a mathematical model to the data Linear, Quadratic, Exponential, Logarithmic, etc. Describes the relationship mathematically (with an equation)

Correlation A measure that quantifies the strengths of the relationship between the variables Linear Model Strong or weak positive correlation Strong or weak negative correlation Draw four examples (one of each)

Correlation (con’t) R value – correlation coefficient R = 0  no correlation R = ±1  perfect positive / negative correlation Perfect means all points are on the line!! All Models (quad, exp, log, linear, etc.) R2 value – gives a measure of strength of the relationship R2 = 0.4 indicates that 40% of the variation in y is related to the variation in x

NOTE!! A strong R2 does not mean cause and effect. It only means that the variables are related!!

Residuals One way to analyze the “goodness of fit” of a model The vertical distance between a point and the line of best fit is it’s residual value The residuals can be graphed and used to illustrate / judge the appropriateness of the model

Residuals Example

Residuals – Look Fors If the residuals are small and there is no noticeable pattern, then the model is a good fit. A noticeable pattern may indicate a better choice of model (e.g. quadratic instead of linear). If a few pieces of data occur as large residuals they can be ignored.