1. Residuals and Residual Plots Most likely a linear regression will not fit the data perfectly. The residual (e) for each data point is the ________________________ from the data point to the regression line. It is the error in __________________. To find the residual (e) of a data point, take the ________________________ and subtract the __________________________ (y value from the linear regression). The sum of the residuals is equal to _____. That is, Σ e = Residuals can be plotted on a scatterplot called a ____________________________.  The horizontal x-axis is the same ________________________ as the original graph.  The vertical y-axis is now the ________________________. LOOKING AT RESIDUAL PLOTS:  When a set of data has a linear pattern, its residual plot will have a ____________________________.  If a set of data does not have a linear pattern, its residual plot will _______________________, but rather, will have a _____________. HOW TO USE RESIDUAL PLOTS:  If the residual plot is RANDOM:  If the residual plot is NON-random: distance prediction observed y value predicted value zero Residual Plot x value residual random pattern NOT be random shape Use Linear Regression DO NOT USE Linear Regression Consider some other type of regression.

2. Perfectly Linear Data Draw a scatterplot from the given data. Enter x-values into L1. Enter y-values into L2. Use a calculator to find the linear regression for this data. LinReg y=ax+b a= b= r 2 = r= Linear regression equation: Draw the linear regression on the same graph as the scatter plot (left). Enter linear regression into Y 1. Use the table feature on the calculator to fill in the center column on the residual table (top right). Complete the table. Create a residual plot (right). What do you notice about the residual plot? How does the linear regression fit the data?

3. Linear Data A scatterplot and linear regression line are already drawn from the given data. Enter x-values into L1. Enter y-values into L2. How does the linear regression fit the data? Use a calculator to find the linear regression for this data. LinReg y=ax+b a= b= r 2 = r= Linear regression equation: Enter linear regression into Y 1. Use the table feature on the calculator to fill in the center column on the residual table (top right). Complete the table. Create a residual plot (right). What do you notice about the residual plot?

4. Non- Linear Data A scatterplot and linear regression line are already drawn from the given data. Enter x-values into L1. Enter y-values into L2. How does the linear regression fit the data? Use a calculator to find the linear regression for this data. LinReg y=ax+b a= b= r 2 = r= Linear regression equation: Enter linear regression into Y 1. Use the table feature on the calculator to fill in the center column on the residual table (top right). Complete the table. Create a residual plot (right). What do you notice about the residual plot?