Difference between revisions of "De Veaux Map"
From Sean_Carver
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* 7.4 Regression to the Mean | * 7.4 Regression to the Mean | ||
| − | :::Etiology of the | + | :::Etiology of the word "Regression" |
:::Math Box: Derivation of regression formula | :::Math Box: Derivation of regression formula | ||
* 7.5 Examining the Residuals | * 7.5 Examining the Residuals | ||
Revision as of 18:36, 17 November 2018
Contents
Part I: Exploring and Understanding Data
Chapter 1: Exploring and Understanding Data =
- 1.1: What is Statistics?
- 1.2: Data
- 1.3: Variables
- Types of Variables: Categorical, Quantitative, Identifier, Ordinal
Chapter 2: Displaying and Describing Categorical Data
- 2.1: Summarizing and Displaying a Single Categorical Variable
- The area principle
- Frequency tables
- Bar charts
- Pie charts
- 2.2: Exploring the Relationship Between Two Categorical Variables
- Contingency tables
- Conditional distributions
- Independence
- Plotting conditional distributions (with pie charts, bar charts and segmented bar charts)
Chapter 3: Displaying and Displaying Quantitative Data
- 3.1: Displaying Quantitative Variables
- Histograms
- Stem and leaf displays
- Dotplots
- 3.2: Shape
- Unimodal, bimodal or multimodal
- Symmetric or skewed
- Outliers
- 3.3: Center
- Median
- 3.4: Spread
- Range, min, max
- Interquartile range, Q1, Q3
- 3.5: Boxplots and 5-Number Summaries
- 3.6: The Center of a Symmetric Distribution: The Mean
- Mean or Median?
- 3.7: The Spread of a Symmetric Distribution: The Standard Deviation
- 3.8: Summary---What to Tell About a Quantitative Variable
Chapter 4: Understanding and Comparing Distributions
- 4.1: Comparing Groups with Histograms
- 4.2: Comparing Groups with Boxplots
- 4.3: Outliers
- 4.4: Timeplots
- 4.5: Re-Expressing Data: A First Look
- ...To improve symmetry
- ...To equalize spread across groups
Chapter 5: The Standard Deviation as a Ruler and the Normal Model
- 5.1: Standardizing with z-Scores
- 5.2: Shifting and Scaling
- Shifting to adjust the center
- Rescaling to adjust the scale
- Shifting, scaling and z-Scores
- 5.3: Normal Models
- The "nearly normal condition"
- The 68-95-99.7 Rule
- 5.4: Finding Normal Percentiles
- Normal percentiles
- From percentiles to scores: z in reverse
- 5.5: Normal Probability Plots
Part II: Exploring Relationships Between Variables
Chapter 6: Scatterplots, Association, and Correlation
- 6.1: Scatterplots
- Direction (negative or positive)
- Form
- Strength
- Outliers
- Explanatory and response variables
- 6.2: Correlation
- Formula
- Assumptions and conditions for correlation, including...
- "Quantitative variables condition,"
- "Straight enough condition,"
- "No outliers condition"
- 6.3: Warning: Correlation Does Not Equal Causation
- 6.4: Straightening Scatterplots
Chapter 7: Linear Regression
- 7.1 Least Squares: The Line of "Best Fit"
- The linear model
- Predicted values and residuals
- The least squares line and the sense in which it is the best fit
- 7.2 The Linear Model
- Using the linear model to make predictions
- 7.3 Finding the Least Squares Line
- Formulas for slope and intercept
- 7.4 Regression to the Mean
- Etiology of the word "Regression"
- Math Box: Derivation of regression formula
- 7.5 Examining the Residuals
- Formula for residuals
- Appropriate (lack of) form of Residuals versus x-Values plot
- The residual standard deviation
- 7.6 R^2---The Variation Accounted For by the Model
- How big should R^2 be?
- Predicting in the other direction---A tale of two regressions
- 7.7 Regression Assumptions and Conditions
- "Quantitative variable" condition
- "Straight enough" condition
- "Outlier" condition
- "Does the plot thicken?" condition
- Judging the conditions with the residuals-versus-predicted-values plot
