1. Midterm Review! Unit I (Chapter 1-6) – Exploring Data Unit II (Chapters 7-10) - Regression Unit III (Chapters 11-13) - Experiments Unit IV (Chapters 14-17) - Probability

2. Unit 1 (Chapters 1-6) Exploratory Data Analysis

3. Key Ideas Identifying types of variables Describe Data with numbers, graphs and words (CUSS – Center, shape, spread, unusual features) Comparing two data sets (CUSS) Resistant vs. non-resistant statistics Finding Outliers Picking the right graph for your data Contingency tables – Marginal & conditional totals Normal

4. Identifying types of variables Variables you can average, and it make sense to do so Variables which fit into categories

5. CUSS Center Unusual Shape Spread

6. CUSS Be sure that if you talk about mean, then you also talk about…. Similarly for median…

7. Describing a distribution

8. Example – comparing using CUSS

9. Resistant Classify the following as resistant/non-resistant: Mean Median Mode Standard Deviation IQR Range r R^2

10. Potential Outliers – How do I find ‘em? Look: 1.5*IQR (must memorize) Look at SD’s – more than 2 away for normal distributions, more than 3 if we don’t know what the distribution looks like

11. Choosing a graph – advantages/disadvantages Dotplots Box&Whisker Stem & leaf Histogram Ogives (cumulative frequency)

12. Contingency Table

13. Normal Models

15. Unit 1 (Chapter 1-6) Calculator Stuff Put values in lists Create: Histogram Do 1-VarStats – find Mean, standard deviation (which one to use?) 5 number summary Normalcdf(low z, high z) InvNorm(area to LEFT of cut point)

16. Chapters 1-6 I can do by hand: Use a 5 number summary to create a boxplot Find outliers using 1.5IQR rule Use a boxplot to create a 5-number summary Create & interpret a stem & leaf plot

17. Hot Tips Know how the mean follows the skewness, but the median doesn’t. Be ready to crank out the outlier test given only Q1 and Q3. Compare shapes, compare centers (using mean or median), and compare spreads (using standard deviation or IQR). Use context. Remember, the y-axis on a histogram show frequency, not data. If you are going to discuss how unusual a data point is, use IQR or standard deviation to compare it to the center. Know how to use InvNorm – you are finding the z-score for the area to the LEFT of your cut point.

18. Unit I Key Problems Chapter 3 #5, 15, Chapter 4 #5, 15, 19, 29, Chapter 5 #13, 23 (outlier test for b!), 25, 29, 31

19. Unit I (Chapters 1-6) Vocab Categorical variableHistogramBoxplot Quantitative variableStemplotDotplot Pie ChartRelative FrequencyFrequency Table Marginal DistributionConditional DistributionModified Boxplot Bar ChartCumulative Freq Plot (Ogive)Skewed Left/Right UniformUnimodalBimodal Skewed left/right5-number summaryIQR Quartile(s)VarianceRange

20. Unit 2 Review Chapters 7-10 Scatterplots and Regression

21. Key Concepts Describe a scatterplot IN CONTEXT - SUDS (Shape, unusual features, direction, Strength). Use r if you have it. Be able to interpret regression given computer print out Interpret in context: Slope Y-intercept R^2 (CoD) Correlation coefficient (r) S (standard deviation of residuals) Find a residual and interpret its meaning

22. More Key concepts Outliers and influential points Non-resistance of r and LSRL Why we call an LSRL and LSRL The importance of residual plots – what do they tell us? Using logs, ln’s, etc. to linearize Be careful with wording!

23. SUDS

24. Computer Output Regression Analysis: IQ versus Time in KY (in years) Predictor Coef SE Coef T P Constant 129.092 5.996 21.53 0.000 Time -5.196 1.146 -4.54 0.001 S = 13.1089 R-Sq = 69.6% R-Sq(adj) = 66.2% Analysis of Variance Source DF SS MS F P Regression 1 3536.0 3536.0 20.58 0.001 Residual Error 9 1546.6 171.8 Total 10 5082.5

25. Residuals and why LSRL

26. Why Residuals Plots are important

27. Outliers, resistance or r and LSRL

28. Re-expressing data Know how to work with something like: log(y-hat) = 2.3 log(x) + 4 You won’t have to figure out how to re-express Know how to interpret R^2 for the above equation (say R^2 = 85%) Be able to look at residual plots of multiple re- expressions and determine which is the best.

29. Unit II Calculator Stuff LinReg – gets RESID list Enter data and find equation of LSRL, r, R^2 Create scatterplot and residual plot

30. Hot tips Computing a residual from a point and the LSRL is very common. The list of stuff to interpret in context is common, too. Un-doing a transformed LSRL (chapter 10) should be easy (Ch. 10 #1) Make sure you don’t just write x and y for an equation. Define them in context. It is highly doubtful you will need to find the LSRL or the residual plot on your calculator—it is essential that you can read the LSRL from computer output and be able to interpret a given residual plot. Don’t forget that r not only tells you the strength of the linear relationship, it also tells you whether it’s positive or negative. Make sure to include that fact in any interpretation of r.

31. Unit II Key Problems Chapter 7 # 1, 5, 11, 17 Chapter 8 # 5, 7, 9, 35 Chapter 9 #1, 11, Chapter 10 # 2 Good to REALLY make sure you have it down: Chapter 7 #9 (Tricky like an AP question) Chapter 8 #1ab Chapter 10 #1