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Midterm Review!

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. Unit 1 (Chapters 1-6). Exploratory Data Analysis. Key Ideas. Identifying types of variables

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Midterm Review!

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  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

  14. 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

  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

  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

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