Homework: PG. 204 #30, 31 pg. 212 #35,36 30.) a. Reading scores are predicted to increase by 0.882 for each one-point increase in IQ. For x=90: 45.98; For x=130: 81.26 Can be done by plotting (90,45.98) and (130, 81.26), then drawing the line connecting them The intercept would correspond to the expected reading score for a child with IQ of 0. 31.) A. 0.0138 The length of the dive is predicted to increase by 0.0138 minutes for each additional meter of depth. B.) 5.45 C.) Plot two points and connect it.

35.) A. BAC=-0.0127+0.017964(#of Beers) B. On average, the BAC will increase by 0.017964 for each additional beer consumed. The average BAC will be -0.01270 if no beers are consumed. C. 0.0951 D. 0.0049 36.) A. Positive, linear, and very strong B. 500 cubic feet of gas per day C. It is called the “least-squares line” because it minimizes that sum of the squares of the errors of the observed amounts to the predicted amounts. D. The LSRL fits because the prediction errors are very small and the linear relationship is very strong.

Example: pg. 204 #29 Some data were collected on the weight of a male lab rat following its birth. The linear regression equation is weight=100+40(time). A.) Interpret the slope in this setting. B.) Interpret the y intercept in this setting. C.) Draw a graph of this line between birth and 10 weeks of age. D.) Would you be willing to use this line to predict the rat’s weight at age 2 years?

3.2 r2 and residuals

R2 and residuals r2—percent of the variation in y that is explained by the LSRL on x. Coefficient of determination “55% of variation in height can be predicted by our regression equation, given hand span” Residual: observed—predicted residual plot—scatterplot of the regression residuals against the explanatory variable Helps assess how well a regression line fits the data

Measure your hand span and height Draw scatterplot In notes. Draw blank residual plot next to it. Compare with calculator.

Residual plot Make a residual plot of height/hand data Why negative and positive values? What does this show you? What if you get a pattern?

Residual plot Shows how linear the relationship is —WANT scattered Points far away from 0 (vertically) are outliers If the residuals make a curved pattern— straight line may not be the best model for the data

Influential Outliers If you remove it and it changes your calculations drastically. Example: Correlation data from 2 days ago: r=0.48 Without the point (10,1), r=0.99 The point (10,1) would be an influential outlier. X: 1 2 3 4 10 Y: 5 11

HW: pg 227 #43-44, 47-48