Difference between revisions of "De Veaux Map"

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(→‎Chapter 6: Scatterplots, Association, and Correlation)
(→‎Chapter 7: Linear Regression)
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* 7.1 Least Squares: The Line of "Best Fit"
 
* 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
 
* 7.2 The Linear Model
 +
:::Using the linear model to make predictions
 
* 7.3 Finding the Least Squares Line
 
* 7.3 Finding the Least Squares Line
 +
:::Formulas for slope and intercept
 
* 7.4 Regression to the Mean
 
* 7.4 Regression to the Mean
 +
:::Etiology of the work "Regression"
 +
:::Math Box: Derivation of regression formula
 
* 7.5 Examining the Residuals
 
* 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
 
* 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
 
* 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

Revision as of 18:32, 17 November 2018

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 work "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
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