Day 13 Agenda: DG6 --- 15 minutes

Section 3.2: Least Squares Regression AP STAT Section 3.2: Least Squares Regression Part 3: Interpreting Residual Plots EQ: How do you use Residual Plots to assess how well a LSRL fits a data set?

---scatterplot of the regression residuals against the predicted value; assess how well a LSRL fits Residual Plots LINEAR ASSOCIATION: No Pattern Evident Pattern Evident NONLINEAR ASSOCIATION:

Ex 1: No pattern evident in the residual plot, linear association appropriate

Ex 2: No pattern evident in the residual plot, linear association appropriate

Ex 3: Pattern evident in the residual plot, linear association not appropriate.

Ex 4: Pattern evident in the residual plot, linear association not appropriate.

Ex 5: Pattern evident in the residual plot, linear association not appropriate.

Ex 6: Pattern evident in the residual plot, linear association not appropriate. An increasing trend in residuals as explanatory values increase.

The AP Stat exam will present residual plots with very obvious patterns. They are not trying to trick you. They want to make sure you understand the purpose of a residual plot.

No pattern evident. Ex 7: Although a linear model seems be appropriate, there appear to be too many _____________residuals, implying this line_________________ the data. negative overestimates

No pattern evident. Ex 7: Although a linear model seems be appropriate, there appear to be too many _____________residuals, implying this line_________________ the data. positive underestimates

Use your graphing calculator to create a residual plot using NEA and FAT. To make sure the LAST regression equation your calculator found was for NEA vs FAT, recalculate the scatterplot and the LSRL for NEA vs FAT. Now the residuals for this plot are stored in a list called RESID.

Use your graphing calculator to create a residual plot using NEA and FAT. Go to Y1 and deactivate the LSRL by entering on the “=“ sign.

Use your graphing calculator to create a residual plot using NEA and FAT. Go to STATPLOT and cut off PLOT1 and cut on PLOT2. Select the first graph. Choose NEA as Xlist and RESID as Ylist.

RESID is the list of the LAST RESIDUALS your calculator created. Use your graphing calculator to create a residual plot using NEA and FAT. RESID is the list of the LAST RESIDUALS your calculator created. ZOOM9 Compare to Residual Plot on p. 219.

SCATTERPLOT LSRL RESIDUAL PLOT You must make reference to ALL displays presented to you. You will need notebook paper to answer this question.

RESIDUAL PLOT SCATTERPLOT LSRL Since the scatterplot shows several data points not following the trend of this LSRL, this model may not be the best fit for our data.

RESIDUAL PLOT SCATTERPLOT LSRL The regression analysis shows the coefficient of determination as .606, indicating only approximately 60.6% of the variation in predicted kg of fat gain is accounted for by this LSRL of fat gain on nonexercise activity. This model may not be the best fit for this data.

SCATTERPLOT LSRL RESIDUAL PLOT Although the residual plot shows data points randomly scattered with no pattern evident, there are smaller residuals at the lower caloric values of NEA. Then, as the caloric values increase, the residuals increase and there appear to be more residual points below the regression line. This would be another indicator that this LSRL may not be the best model for this data.

MUST HIT Points When Deciding Upon a Linear Association: [DON'T RELY ON JUST ONE] 1. Observe Scatterplot for Linearity 2. State Correlation Coefficient --- strong vs weak 3. State Coefficient of Determination --- good fit vs not a good fit 4. Observe Residual Plot --- pattern (nonlinear) vs no pattern (linear)

Normal Probability Plot Know the Difference Between a Normal Probability Plot and a Residual Plot Is Normal Distribution appropriate? Normal Probability Plot Is Linear Model appropriate? Residual Plot

Assignment : pp. 220 - 222 #39, 40, 42 pp. 227 - 228 #43, 44, 47, 48 pp. 230 - 233 #49 - 51, 53, 55