1. Ch. 10 Correlation and Regression 10-3 Notes Inferences for Correlation and Regression

2. Focus Points - Test the ______________________________. -Use sample data to compute the _____________ ________________________________________. -Find a ____________________ for the value of y predicted for specified value of x. -Test the ____________ of the least-squares line. -Find a ___________________ for the slope β of the least squares line and interpret its meaning.

3. Population Correlation Coefficient (ρ) is typically unknown, just like μ. In statistics we use a random sample from the population and calculate the correlation for the sample. If the correlation is strong enough for the sample, then we may conclude that the population has a correlation. Steps 1Establish H 0 and H 1. H 0 : (always) H 1 : (choose one) 2Find the critical region. Use t-Distribution where d.f. = ______ where n = ____________________________________. 3Use _________________ to find your sample statistic. 4Draw conclusion a) ________; we are ?% confident that H 1, therefore there is a (+, –, or *either way) correlation between x and y. b________________; at α = ?% the evidence is not strong enough to imply H 1, therefore there is no significant (+, –, or *either way) correlation between x and y.

4. Ex. 1A medical research team is studying the effect of a new drug on red blood cells. Let x be a random variable representing milligrams of the drug given to a patient. Let y be a random variable representing red blood cells per cubic milliliter of whole blood. A random sample of n = 7 volunteer patients gave the following results. Use α = 0.05 to test for any correlation between the drug and red blood cell count. Steps 1H 0 : H 1 : 2t 0 = See Table 7 using d.f. =, α = 0.05, and 2-tailed test (≠) 3t ≈ 4Conclusion: (different from 0) x9.210.19.012.58.89.19.5 y5.04.84.55.75.14.64.2

5. Residual – the difference between an ________ value of y and the corresponding ____________ value. Standard error of estimate S E – the standard deviation of the _____________. To find S E, use __________ and arrow down to s. s = S E

6. Confidence Intervals for Prediction Recall from 10-2 Notes the following example. Ex. 1 The number of workers on an assembly line varies due to the level of absenteeism on any given day. In a random sample of production output from several days of work, the following data were obtained, where x = number of workers absent from the assembly line and y = number of defects coming off of the line. x35021 y162091210 y = 8.257 + 2.338x

7. When making a prediction for y using the least squares line, the prediction lies on the least squares line. However, we know that not all values (if any) lie on the line. Therefore, we build an interval around our prediction that allows us to be a certain percent confident that the result will be within our interval. Formula: for t c use d.f. = n – 2 where n = # of ordered pairs where, Σx 2, and Σx can all be found by doing 1-Var Stats

8. Recall: d) On a day when 4 workers are absent from the assembly line, what would the least-squares line predict for the number of defects coming off the line? yp = 8.257 + 2.338 (4) = Ex. 1 Find a 90% confidence interval for the forecast y value in part d. where Using 1Var Stat = Σx 2,= Σx = n =

9. Assignment Day 1 p. 543 #1, 7, 9, 10 For 7, 9, 10 do parts a-e. For e, also explain its meaning in context.

10. Testing the slope β of the least squares line is the same as for correlation coefficient ρ except: For H o and for H 1 we use ___ instead of ___. Ex. 3How fast do puppies grow? That depends on the puppy. How about male wolf pups in the Helsinki Zoo (Finland)? Let x = age in weeks and y = weight in kilograms for a random sample of male wolf pups. The following data are based on the article Studies of the Wolf in Finland Canis lupus L by E. Pulliainen, University of Helsinki. x8101420284045 y7131723303435

11. a) Use α = 1% to test the claim that β ≠ 0, and interpret the results in the context of this application.

12. Finding a Confidence Interval for β is similar to finding a Confidence Interval for y p except that the formula for E varies slightly. where

13. b) Still using the data from ex. 3, compute an 80% Confidence Interval for β and interpret the results in the context of this application.

14. Assignment Day 1 p. 544 #7, 9, 10 f & g; also do #11 all