Title The manga guide to regression analysis 13.9 MB 235
```                            Preface
Prologue
More Tea?
1
A Refreshing
Glass of Math
Building a Foundation
Inverse Functions
exponents and logarithms
Rules for exponents and logarithms
Differential calculus
Matrices
Multiplying Matrices
The Rules of Matrix Multiplication
Identity and Inverse Matrices
Statistical Data Types
Hypothesis Testing
Measuring Variation
Sum of Squared Deviations
Variance
Standard Deviation
Probability Density Functions
Normal Distributions
Chi-Squared Distributions
Probability Density Distribution Tables
F Distributions
2
Simple
Regression
Analysis
First Steps
Plotting the Data
The Regression Equation
General Regression Analysis Procedure
step 1: Draw a scatter plot of the independent variable versus the dependent variable. If the dots line up, the variables may be correlated.
Step 2: Calculate the regression equation.
Step 3: Calculate the correlation coefficient (R ) and assess our population and assumptions.
Samples and Populations
Assumptions of Normality
Step 4: Conduct the analysis of variance.
Step 5: Calculate the confidence intervals.
step 6: Make a prediction!
Which Steps Are Necessary?
Standardized Residual
Interpolation and Extrapolation
Autocorrelation
Nonlinear Regression
Transforming Nonlinear Equations into Linear Equations
3
Multiple
Regression
Analysis
Predicting with Many Variables
The multiple regression equation
Multiple Regression Analysis Step-by-Step
step 1: draw a scatter plot of each predictor variable and the outcome variable to see if they appear to be related.
step 2: calculate the multiple regression equation.
Step 3: Examine the accuracy of the multiple regression equation.
The Trouble with R2
hypothesis testing with multiple regression
Step 4: Conduct the Analysis of Variance (ANOVA) Test.
Finding S11 and S22
Step 5: calculate Confidence intervals for the population.
step 6: Make A Prediction!
choosing the best combination of Predictor variables
Assessing Populations with
Multiple Regression Analysis
Standardized Residuals
Mahalanobis Distance
Step 1
Step 2
Step 3
Using Categorical Data in Multiple Regression analysis
Multicollinearity
determining the Relative Influence of Predictor Variables on the Outcome Variable
4
Logistic
Regression
Analysis
The Final Lesson
the maximum likelihood method
Finding the maximum likelihood Using the Likelihood Function
Choosing Predictor variables
Logistic regression analysis in Action!
Logistic Regression Analysis Step-by-Step
Step 1: draw a scatter plot of the predictor variables and the outcome variable to see whether they appear to be related.
Step 2: calculate the logistic regression equation.
Step 3: assess the accuracy of the equation
Step 4: conduct the hypothesis tests.
Step 5: Predict whether the Norns special will sell.
Logistic Regression Analysis in the Real World
Logit, Odds Ratio, and Relative Risk
Logit
Odds Ratio
Hypothesis Testing with Odds
Confidence Interval for an Odds Ratio
Relative Risk
A
Regression Calculations with Excel
Euler’s Number
Power
Natural Logarithm
Matrix Multiplication
Matrix Inversion
Calculating a Chi-Squared Statistic from a p-Value
Calculating a p-Value from a Chi-Squared Statistic
Calculating an F Statistic from a p-Value
Calculating a p-Value for an F Distribution
Partial Regression Coefficient of a Multiple Regression Analysis
Regression Coefficient of a Logistic Regression Equation
Index
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