1. Inference for Regression Find your notes from last week, Put # of beers in L1 and BAC in L2, then find LinReg(ax+b)

2. Confidence Interval: the standard error of the least squares slope, b Formulas: df = n -2 Because there are two unknowns  & 

3. Interpretation: We are 95% confident that the mean change in BAC per beer is between ___________ and _____________

4. Back to our Example: For a study on student drinking and blood alcohol level, sixteen student volunteers at Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC). The results are show below: a)Find the LSRL, correlation coefficient, and coefficient of determination. BAC = -.0127 + 0.018 (Beers) r = 0.8943 r 2 = 0.7998

5. b) Explain the meaning of slope in the context of the problem. There is approximately 1.8% increase in BAC for every Beer c) Explain the meaning of the coefficient of determination in context. Approximately 80% of the variation in BAC can be explained by the regression of BAC on number of Beers drunk.

6. d) Estimate , , and .  = -.0127  =.0180  =.0204 e) Create a scatter plot, residual plot and box plot of the residuals for the data. Beers BAC Beers Residuals

7. the standard error of the least squares slope, b

8. f) Give a 95% confidence interval for the true slope of the LSRL. Assumptions: Have an SRS of students Since the residual plot is randomly scattered, BAC and # of beers are linear Since the points are evenly spaced across the LSRL on the scatterplot,  y is approximately equal for all values of BAC Since the boxplot of residual is approximately symmetrical, the responses are approximately normally distributed. We are 95% confident that the true slope of the LSRL of weight & body fat is between 0.12 and 0.38. Be sure to show all graphs!

9. Frappy

13. Formulas: Hypothesis test:

14. Hypotheses H 0 :  = 0 H a :  > 0 H a :  < 0 H a :  ≠ 0 This implies that there is no relationship between x & y Or that x should not be used to predict y What would the slope equal if there were a perfect relationship between x & y? 1 Be sure to define  !

15. Median SAT ExpenditureGrad Rate 1065797049 950640133 1045628537 990679249 950454122 970718638 980773639 1080638252 1035732353 1010653141 1010621638 930737537 1005787445 1090635557 1085626148 The data on six-year graduation rate (%), student-related expenditure per full-time student, and median SAT score for a random sample of the primarily undergraduate public universities in the US with enrollments between 10,000 and 20,000 were taken from College Results Online, The Education Trust. We would like to know if there is. For a test of a linear relationship, the null hypothesis is usually expressed as: In this context, this means

16. Conjecture: We suspect that increased expenditures can be used to predict graduation rates. H 0 :  = 0 Where  is the true slope between expenditures and graduation rates. H a :  > 0

17. Assumptions: Have an SRS of colleges Since the residual plot is randomly scattered, Expenditures and Grad rates are linear Since the points are evenly spaced across the LSRL on the scatterplot, s y is approximately equal for all values of grad rate Since the boxplot of residual is approximately symmetrical, the responses are approximately normally distributed.

18. Test statistic: Linear Regression t-test

19. Since the p-value < a, I reject H 0. There is sufficient evidence to suggest that expenditures can be used to predict graduation rate.