1. Stat 350 Lab Session GSI: Yizao Wang Section 016 Mon 2pm30-4pm MH 444-D Section 043 Wed 2pm30-4pm MH 444-B

2. Today’s Agenda Review on scatterplot and linear regression Module 10 Activity 1 and 2 Return Exam 2 Please log in with UMID for today’s qwizdom questions. Your participation will be graded based on the number of questions you answer.

3. Second Midterm Summary 2 nd midtern exam more difficult than the 1st Mean scores: lab016 57.3/lab043 56.2 (all labs: 55.3) Deadline for checking scores: Friday April 11 th Come to Yizao for totaling errors. Otherwise ask your lecture instructor.

4. Scatterplots A Scatterplot displays the relationship between two quantitative variables –X: explanatory/predictor/independent variable –Y: response or dependent variable Things to look for in Scatterplots –Form: linear, curved, clusters,… –Direction: positive or negative –Strength: how close points are to the underlying form (weak, moderate, strong, etc. ) –Outliers or other deviations from this overall pattern

5. Scatterplots - #1, #2, and #3 show linear relationship. - #1 and #2 show positive direction, but #3 shows negative direction. - #2 shows stronger strength comparing to #1. #4 has a curved form.#5 has a clustered form.#6 has outliers.

6. Regression Model Population version: y i =  0 +  1 x i +  i where the  i are i.i.d. N (0,  ), seen as measurement errors or noise.  0 and  1 are parameters, fixed but unknown constants, called intercept and slope, respectively. Sample version: ŷ i = b 0 + b 1 x i b 0 and b 1 are estimated intercept and slope respectively.

7. About Correlation Correlation r (or R) (1  r  1) measures the strength of linear association between two variables and direction Roughly, |r| > 0.7 => strong R 2 (0  R 2  1) measures the proportion of the variation in the response that can be explained by the linear regression of Y on X Roughly, R 2 > 0.5 => strong

8. Examples of Correlation

9. How to Use the Yellow Card Make sure you understand (and know how to calculate) the following terms: S XY, S XX, S YY Residual e = observed y – predicted y SSTO, SSM (SSREG), SSE The inference part of linear regression: HT, CI, PI…

10. Which variable is the response? Poverty Rate Teen Birth Rate

11. Which variable is the explanatory variable? Poverty Rate Teen Birth Rate

12. Yes or No Based on the scatterplot, does there appear to be a linear relationship between teen birth rate and poverty rate?

13. Think about the strength and direction of the relationship. Which of the following do you think is most reasonable for the value of the correlation coefficient? -0.6 0.2 0.7 None of the above

14. What is the estimated regression line? Predicted_TeenBrth = 15.674 + 2.025(PovPct) Predicted_TeenBrth = 2.025 + 15.674(PovPct) PovPct = 15.674 + 2.025(Predicted_TeenBrth) PovPct = 2.025 + 15.674(Predicted_TeenBrth)

15. What output could be used to help determine the value of the correlation coefficient? A)Model Summary > R B)Model Summary > R Square C)Coefficients > Standardized Coefficients Beta D)All of the above

16. What is the correct interpretation of r 2 ? A)49.5% of teen birth rates can be accounted for by the poverty rate. B)49.5% of the variation in teen birth rate can be accounted for by the linear relationship between teen birth rate and poverty rate.

17. What is the predicted teen birth rate of Michigan (with a poverty rate of 12.2%)? A)24.705 B)40.380 C)193.25 D)Can’t calculate this number

18. Output for Homework 11 Generate regression outputs for homework 11: scatterplot and regression tables...