REGRESSION MODELS OF BEST FIT Assess the fit of a function model for bivariate (2 variables) data by plotting and analyzing residuals.

SCATTER PLOTS  The picture models the shape of the function. (linear, quadratic, exponential, or none)

SHAPED FUNCTIONS  It is possible to use different shaped functions (curves) to model data. Choosing which curve to use (linear, quadratic, exponential) is easy as long as the scatter plot showed a resemblance to the actual curve. But what if it is unclear as to which curve to choose?  RESIDUALS help to determine if a curve (shape) is appropriate for the data. (linear versus non-linear)

RESIDUAL  A residual is the difference between what is plotted in your scatter plot at a specific point, and what the regression equation predicts “should be plotted” at this specific point. If the scatter plot and the regression equation “agree” on a y-value (no difference), the residual will be zero.  RESIDUAL = Actual y-value (from scatter plot) – Predicted y-value (from regression equation line)

CORRELATION COEFFICIENT  The quantity, called the correlation coefficient, measures the strength and the direction of the relationship between two variables. The value is such that it is  The mathematical formula for computing is:

RESIDUAL PLOT  When you look at your scatter plot, and you are unsure if the shape (curve) you chose for your regression equation will create the best model, a RESIDUAL PLOT will help you make a decision as to whether the model you chose will, or will not, be an appropriate linear model.  RESIDUAL PLOT: a scatter plot that shows the residuals on the vertical axis and the independent variable on the horizontal axis

RESIDUAL PLOT  When a pattern is observed in a residual plot, a linear regression model is probably not appropriate for your data.  Appropriate linear model: when plots are randomly placed, above and below the x-axis (y = 0)  Appropriate non-linear model: when plots follow a pattern, resembling a curve 

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