Homework: pg. 180 #6, 7 6.) A. B. The scatterplot shows a negative, linear, fairly weak relationship. C. long-lived territorial species

7.) A. Students with higher IQs tend to have higher GPAs and those with lower IQs generally have lower GPAs. The plot shows a positive association. Roughly linear and moderately strong IQ: about 103; GPA: about 0.5.

Homework: pg. 194 #16, 18 16.) A. Clearly positive but not near 1. Students with high IQs tend to have high grade point averages, but there is more variation in the grade point averages for students with moderate IQs. B. Closer to 1. The overall positive relationship between calories and sodium is stronger than the positive association between IQs and GPAs. C. Removing the outlier in Figure 3.4 would increase r. Removing the outlier in Figure 3.8 would decrease r.

18.) A. R=-0.748 Adding point A: r=-0.807. Adding point B: r=-0.469. Point A fits in with the negative linear association displayed by the other points. However, point B deviates from the pattern, weakening the association.

3.2 Least-Squares Regression Lines

Regression Line regression line—straight line that describes how a response variable changes as an explanatory variable changes **need an explanatory & response variable Use a regression line to predict the value of y given the value of x

Let’s Collect Data! Measure your hand span in cm and your height in inches. Write your stats on the board. (1 inch = 2.54 cm)

Least-Squares Regression Line Make scatterplot and least-squares regression line on calculator Scatterplot—pg 184 LSRL—pg 210-211

Regression Line predicted observed Error = observed – predicted

Least-Squares Regression Line least-squares regression line—minimizes the sum of the squares of the errors Line that makes the sum of the squared vertical distances of the data points from the line as small as possible

Least-Squares Regression Line y-intercept slope 1) The point is on the least squares line 2) We write equation with variable names

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?

HW: pg 204 #30, 31 PG 212 #35, 36