Warm-up O Turn in HW – Ch 8 Worksheet O Complete the warm-up that you picked up by the door. (you have 10 minutes)

Objective O Define and create Residual Plots. (By hand and in the calculator. O Use Residual Plots to determine if using a linear model is appropriate. O Define and calculate R 2 (Coefficient of Determination). O Use R 2 to explain how much of the variation is accounted for by the model.

Residuals O The difference between an observed value of response variable and value predicted by the regression line..

Residuals o Negative residual means the model OVER PREDICTS the y value. o Positive residual means the model UNDER PREDICTS the y value.

Residual Plots O A scatterplot of the residuals against the explanatory variable. O Help us assess how well a regression line fits the data. O Should show no obvious pattern. O Should be relatively small in size

Residual Plot Practice O Do the first page of the Worksheet

Residual Plot (calculator) O Enter x values in L 1 and y values in L 2. O Scroll to put cursor on L 3. Press 2 nd,STAT, Enter, 1. (RESID) This calculates the residuals and puts them in L 3. O Go to STAT PLOT. Turn on Scatterplot. Pick L 1 for X list, and L 3 (RESID) for Y list. ZOOM 9

Residual Plot Practice O Go back to your worksheet. Do # 4 using your calculator to create the scatterplot.

Standard Deviation of Residuals

Coefficient of Determination O R 2 is the fraction of the variation in the values of y that is accounted for by the LSRL of y on x.

Interpreting R 2

Is the linear model appropriate?