Midterm Review!
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Transcript of Midterm Review!
Midterm Review!Unit I (Chapter 1-6) – Exploring Data
Unit II (Chapters 7-10) - RegressionUnit 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 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
Identifying types of variables Variables you can average, and it make sense to
do so
Variables which fit into categories
CUSS Center
Unusual
Shape
Spread
CUSS Be sure that if you talk about mean, then you
also talk about….
Similarly for median…
Describing a distribution
Example – comparing using CUSS
Resistant Classify the following as resistant/non-resistant:
Mean Median Mode Standard Deviation IQR Range r R^2
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
Choosing a graph – advantages/disadvantages Dotplots
Box&Whisker
Stem & leaf
Histogram
Ogives (cumulative frequency)
Contingency Table
Normal Models
Normal Models
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)
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
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.
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
Unit I (Chapters 1-6) VocabCategorical variable Histogram Boxplot
Quantitative variable Stemplot Dotplot
Pie Chart Relative Frequency Frequency Table
Marginal Distribution Conditional Distribution Modified Boxplot
Bar Chart Cumulative Freq Plot (Ogive) Skewed Left/Right
Uniform Unimodal Bimodal
Skewed left/right 5-number summary IQR
Quartile(s) Variance Range
Unit 2 Review
Chapters 7-10Scatterplots and Regression
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
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!
SUDS
Computer OutputRegression Analysis: IQ versus Time in KY (in years)Predictor Coef SE Coef T PConstant 129.092 5.996 21.53 0.000Time -5.196 1.146 -4.54 0.001S = 13.1089 R-Sq = 69.6% R-Sq(adj) = 66.2%
Analysis of VarianceSource DF SS MS F PRegression 1 3536.0 3536.0 20.58 0.001Residual Error 9 1546.6 171.8Total 10 5082.5
Residuals and why LSRL
Why Residuals Plots are important
Outliers, resistance or r and LSRL
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.
Unit II Calculator Stuff LinReg – gets RESID list Enter data and find equation of LSRL, r, R^2 Create scatterplot and residual plot
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.
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