1. Inferences about the slope of the regression line Section 13.2

2. Slope Average or expected change in the y (dependent) variable associated with a 1- unit increase in the x (independent) variable b is the point estimate of

3. Properties of the Sampling Distribution of b It’s normally distributed

4. So….. Estimated standard deviation of b: Test Statistic: (df=n -2)

5. Confidence Interval for (small) implies that the interval is narrow which means there’s relatively precise knowledge of

6. Is cardiovascular fitness related to an athlete’s performance. x7.78.48.799.6 1010.210.41111.7 y7171.46568.764.469.46364.666.962.661.7 95% confident that the true average decrease in ski time associated with a 1 min. increase in treadmill time is between 1 and 3 minutes.

7. Hypothesis Test Why do you think we use 0?

8. x 7.78.48.799.6 1010.210.41111.7 y 7171.46568.764.469.46364.666.962.661.7 Is there a negative association between treadmill time and ski time? Reject the H o. There is sufficient evidence to support the claim that there is a negative association between treadmill time & ski time.

9. Is a runner’s speed related to their steps per second? 90% confidence interval x15.8616.8817.518.6219.9721.0622.11 y3.053.123.173.253.363.463.55

10. Is there relationship between a runner’s speed & their average # of steps per second?

11. Leaning Tower of Pisa Find a 90% confidence interval. Year75777880818283848587 Lean642656667688696698713717725757

12. Leaning Tower of Pisa Test to see if there’s a positive relationship between the year and the amount of leaning. Year75777880818283848587 Lean642656667688696698713717725757