Engineering Data Analysis with Matlab(r)

Cover Half Title Title Page Copyright Page Table of Contents Preface Chapter 1 Getting started 1.1 What is data analysis? 1.1.1 Collecting the data 1.1.2 Importing the data into MATLAB 1.1.3 Data cleaning and transforming 1.1.4 Visualizing the data 1.1.5 Analyzing the data 1.1.6 Visualizing the results 1.2 What is statistical analysis? 1.2.1 Types of data 1.2.1.1 Univariate data 1.2.1.2 Bivariate data 1.2.2 Types of analysis 1.2.2.1 Univariate analysis 1.2.2.2 Bivariate analysis 1.2.2.3 Multivariate analysis 1.3 Statistical analysis in MATLAB 1.3.1 Data visualization in univariate analysis 1.3.2 Data visualization in bivariate analysis 1.3.2.1 Categorical vs. categorical 1.3.2.2 Categorical vs. quantitative 1.3.2.3 Quantitative vs. quantitative 1.3.3 Data Visualization in Multivariate Analysis Chapter 2 Data types and visualization 2.1 Types of data 2.1.1 Qualitative/categorical variables 2.1.1.1 Nominal 2.1.1.2 Ordinal 2.1.2 Qualitative/categorical variables 2.1.2.1 Discrete and continuous 2.1.2.2 Interval and ratio 2.1.3 Types of data in statistical analysis 2.1.3.1 Univariate analysis 2.1.3.2 Bivariate analysis 2.1.3.3 Multivariate analysis 2.2 Collecting the data 2.2.1 Cluster sample 2.3 Data visualization and graphical representation of a variable 2.3.1 Univariate analysis 2.3.1.1 Frequency distribution table 2.3.1.2 Bar chart 2.3.1.3 Pie chart 2.3.1.4 Histogram 2.3.1.5 Boxplot Let’s talk about the box first Lets look at the whiskers now Example Example Example 2.3.2 Scatterplot 2.3.2.1 Example 1 2.3.2.2 Example 2 2.3.2.3 Example 2.3.2.4 Colormap name 2.3.3 Line graphs 2.3.3.1 Plotting 2-D data 2.3.3.2 Example 2.3.3.3 Multiple line graphs 2.3.4 Histogram 2.3.5 Boxplot 2.3.5.1 MATLAB 2.3.5.2 ‘PlotStyle’ 2.3.5.3 ‘BoxStyle’ 2.3.5.4 ‘MedianStyle’ 2.3.5.5 Example 2.3.5.6 Example 2.3.5.7 Example Chapter 3 Random variable and probability distribution 3.1 What is probability? 3.1.1 Independent events 3.1.2 Dependent events 3.1.3 Mutually exclusive events 3.1.4 Mutually inclusive events 3.1.5 Law of total probability 3.1.6 Using both the first Bayes’ theorem and the law of total probability 3.2 Random variable 3.2.1 What is a random variable? 3.2.2 Types of random variables 3.2.2.1 Discrete random variables 3.2.2.2 Continuous random variables 3.2.2.3 MATLAB 3.3 Probability distributions 3.3.1 What is a probability distribution? 3.3.2 Types of probability distribution 3.3.2.1 Discrete probability distribution 3.3.2.2 Continuous probability distribution 3.3.3 Calculating the probabilities in a probability distribution 3.3.3.1 Probability mass function and cumulative density function 3.3.3.2 Probability density function and cumulative density function 3.3.4 Mean and variance of a probability distribution 3.3.4.1 Discrete probability distribution 3.3.4.2 Continuous probability distribution 3.4 Types of discrete and continuous probability distribution 3.5 Probability distributions in MATLAB 3.5.1 Probability distribution object 3.5.1.1 Example 3.5.1.2 Example 3.5.1.3 Example 3.5.1.4 Example 3.5.2 Calculating the probabilities 3.5.2.1 Example 3.5.2.2 Example 3.5.2.3 Example 3.5.2.4 Discrete distribution 3.5.2.5 Continuous distribution 3.5.2.6 Example 3.5.2.7 Example 3.5.2.8 Example 3.5.2.9 Example 3.5.2.10 Examples 3.6 Summary Chapter 4 Discrete probability distribution 4.1 Types of discrete distribution 4.2 Binomial distribution 4.2.1 Calculations in theory 4.2.2 Example 4.2.3 Solution 4.2.3.1 Inverse binomial 4.2.4 Calculations in MATLAB 4.2.4.1 Create a binomial distribution object 4.2.4.2 Fitting the binomial distribution to sample data 4.2.4.3 Use distribution-specific functions 4.3 Bernoulli distribution 4.3.1 Calculations in theory 4.3.2 Calculations in MATLAB 4.4 Multinomial distribution 4.4.1 Calculations in theory 4.4.1.1 Example 4.4.2 Calculations in MATLAB 4.4.2.1 Create a multinomial distribution object 4.4.2.2 Fit the multinomial distribution to sample data 4.4.2.3 Use distribution-specific functions 4.4.2.4 Example 4.5 Hypergeometric distribution 4.5.1 Calculations in theory 4.5.2 Now in MATLAB 4.5.2.1 Create a hypergeometric distribution object 4.5.2.2 Fitting the hypergeometric distribution to sample data 4.5.2.3 Use distribution-specific functions Binomial approximation to the hypergeometric distribution 4.6 Multivariate hypergeometric distribution 4.7 Geometric distribution 4.7.1 Calculations in theory 4.7.1.1 CDF 4.7.1.2 Example 4.7.1.3 Example 4.7.1.4 Example 4.7.1.5 Example 4.7.1.6 Inverse geometric probability distribution 4.7.2 Now in MATLAB 4.7.2.1 Create a geometric distribution object 4.7.2.2 Fitting the geometric distribution to sample data 4.7.2.3 Use distribution-specific functions 4.7.2.4 Example 4.7.2.5 Example 4.8 Negative binomial distribution 4.8.1 Calculations in theory 4.8.1.1 Example 4.8.1.2 Solutions 4.8.1.3 Inverse negative binomial probability distribution 4.8.1.4 Example 4.8.2 Calculations in MATLAB 4.8.2.1 Create a negative binomial distribution object 4.8.2.2 Fitting the negative binomial distribution to sample data 4.8.2.3 Use distribution-specific functions 4.8.2.4 Example 4.8.2.5 Example 4.8.2.6 Example 4.9 Poisson distribution 4.9.1 Calculations in theory 4.9.1.1 Example 4.9.1.2 Inverse Poisson probability distribution 4.9.2 Calculations in MATLAB 4.9.2.1 Create a Poisson distribution object 4.9.2.2 Fitting the Poisson distribution to sample data 4.9.2.3 Use distribution-specific functions 4.9.2.4 Example 4.9.3 Poisson approximation to the binomial distribution 4.9.3.1 Example 4.10 Discrete uniform distribution 4.10.1 Calculations in theory 4.10.1.1 Example 4.10.2 Calculations in MATLAB 4.10.2.1 Fitting the discrete uniform distribution to sample data 4.10.2.2 Use distribution-specific functions 4.10.2.3 Solving the problem in MATLAB 4.11 Summary Chapter 5 Continuous probability distribution 5.1 Types of continuous distribution 5.2 Normal distribution 5.2.1 Why is this important? 5.2.2 How can I check if my data follows a normal distribution? 5.2.2.1 Graphical Tests 5.2.2.2 Statistical tests 5.2.2.3 Parameters of the distribution 5.2.2.4 Shape of the distribution 5.2.2.5 Calculations in theory 5.2.2.6 Examples 5.2.2.7 Calculations in MATLAB 5.3 Lognormal distribution 5.3.1 How can I check if my data follows a lognormal distribution? 5.3.2 Parameters of the distribution 5.3.3 Shape of the distribution 5.3.4 Calculations in theory 5.3.5 Example 5.3.6 Calculations in MATLAB 5.3.6.1 Create a lognormal distribution object 5.3.6.2 Fitting the lognormal distribution to sample data 5.3.6.3 Use distribution-specific functions 5.3.6.4 Example 5.3.6.5 Example 5.4 Gamma distribution 5.4.1 Parameters of the distribution 5.4.2 Shape of the distribution 5.4.3 Compare gamma and normal distribution PDFs 5.4.4 Calculation in theory 5.4.5 Example 5.4.6 Calculations in MATLAB 5.4.6.1 Create a gamma distribution object 5.4.6.2 Fitting the gamma distribution to sample data 5.4.6.3 Use distribution-specific functions 5.4.6.4 Practice questions 5.5 Exponential distribution 5.5.1 Parameters of the distribution 5.5.2 Shape of the distribution 5.5.3 Calculation in theory 5.5.4 Example 5.5.5 Example 5.5.6 Solutions 5.5.7 Calculations in MATLAB 5.5.7.1 Create an exponential distribution object 5.5.7.2 Fitting the gamma distribution to sample data 5.5.7.3 Use distribution-specific functions 5.5.7.4 Example 1 5.5.7.5 Practice problems 5.6 Weibull distribution 5.6.1 Parameters of the distribution 5.6.2 Shape of the distribution 5.6.3 Calculations in theory 5.6.4 Example 5.6.5 Calculation in MATLAB 5.6.5.1 Create a Weibull distribution object 5.6.5.2 Fitting the normal distribution to sample data 5.6.5.3 Use distribution-specific functions 5.6.5.4 Practice problems 5.7 Beta distribution 5.7.1 Parameters of the distribution 5.7.2 Shape of the distribution 5.7.3 Calculations in theory 5.7.4 Example 5.7.5 Calculations in MATLAB 5.7.5.1 Create a beta distribution object 5.7.5.2 Fitting the beta distribution to sample data 5.7.5.3 Use distribution-specific functions 5.7.5.4 Calculations in MATLAB 5.8 Uniform continuous distribution 5.8.1 Parameters of the distribution 5.8.2 Shape of the distribution 5.8.3 Calculation in theory 5.8.4 Example 5.8.5 Solution 5.8.6 Calculation in MATLAB 5.8.6.1 Create a uniform distribution object 5.8.6.2 Use distribution-specific functions 5.8.6.3 Practice examples 5.9 Rayleigh distribution 5.9.1 Parameters of the distribution 5.9.2 Shape of the distribution 5.9.3 Calculations in theory 4.9.4 Example 5.9.5 Calculations in MATLAB 5.9.5.1 Create a Rayleigh distribution object 5.9.5.2 Use distribution-specific functions Solving Example 1 using the above functions: 5.10 Extreme value distribution 5.10.1 Parameters of the distribution 5.10.2 Shape of the distribution 5.10.2.1 Type 1/Gumbel distribution 5.10.2.2 Type 2/Fréchet distribution 5.10.2.3 Type 3/three-parameter Weibull distribution 5.10.3 Calculations in theory 5.10.3.1 Type 1/Gumbel distribution 5.10.3.2 Type 2/Fréchet distribution 5.10.3.3 Type 3/three-parameter Weibull distribution 5.10.4 Calculations in MATLAB 5.10.4.1 Create an extreme value distribution object 5.10.4.2 Use distribution-specific functions 5.10.4.3 Create a Gumbel distribution object Chapter 6 Descriptive statistics 6.1 Main branches of descriptive statistics 6.2 Central tendency 6.2.1 Mean 6.2.1.1 Arithmetic mean 6.2.1.2 Geometric mean 6.2.1.3 Harmonic mean 6.2.2 Median 6.2.2.1 Median for a sample dataset 6.2.2.2 Example 6.2.2.3 Median for a frequency distribution table 6.2.3 Mode 6.2.3.1 Mode for frequency distribution table 6.2.4 Central tendency 6.2.4.1 Example 6.2.4.2 Example 6.3 Measures of dispersion/variability 6.3.1 Range 6.3.2 Mean deviation 6.3.2.1 Sample dataset 6.3.2.2 Frequency distribution table 6.3.2.3 Example  6.3.3 Standard deviation 6.3.3.1 Sample mean vs. population mean 6.3.3.2 Sample dataset 6.3.3.3 Frequency distribution table 6.3.4 Quartile deviation 6.3.4.1 Sample dataset 6.3.4.2 Frequency distribution table 6.3.4.3 or third quartile 6.3.4.4 Empirical relation between measures of variation 6.3.4.5 In MATLAB 6.4 Distribution shape 6.4.1 Skewness 6.4.2 Kurtosis 6.4.2.1 Types of kurtosis 6.4.3 Moments 6.4.3.1 First moment 6.4.3.2 Second moment 6.4.3.3 Third moment 6.4.3.4 Fourth moment 6.4.3.5 For a sample dataset 6.4.3.6 Example 6.4.3.7 Population vs. sample 6.4.3.8 Interpretation 6.4.3.9 Example 6.4.3.10 Interpretation 6.4.3.11 Example 6.4.3.12 Interpretation 6.4.3.13 Example 6.4.3.14 Interpretation 6.4.3.15 For frequency distribution 6.4.3.16 Example 6.4.3.17 Example 6.4.3.18 Calculations in MATLAB 6.4.3.19 MATLAB 6.4.3.19.1 For ungrouped data 6.4.3.20 MATLAB Chapter 7 Inferential statistics 7.1 Sampling distribution 7.1.1 Example 7.2 Central limit theorem 7.3 Hypothesis testing 7.3.1 Hypothesis test terminology 7.3.1.1 First step: Stating the hypothesis 7.3.1.2 Second step: Choose the correct alpha/significance level α 7.3.1.3 Third step: Calculate the test statistic 7.3.1.4 Fourth step: Choosing the approach 7.3.1.5 Fifth step: Making the decision 7.3.1.6 Comparing critical value and p-value approaches 7.3.2 Types of tests 7.3.2.1 Parametric tests 7.3.2.2 Non-parametric tests 7.4 Assessing the population distribution 7.4.1 Visual methods 7.4.1.1 Histogram 7.4.1.2 Q-Q plot 7.4.1.3 Boxplot 7.4.2 Statistical tests 7.4.2.1 Specifying the alpha level 7.5 Statistical tests for normality 7.5.1 The chi-squared goodness of fit 7.5.1.1 Example 7.5.1.2 Calculation in MATLAB 7.5.1.3 Conditions 7.5.1.4 Test statistic 7.5.1.5 Critical value approach 7.5.1.6 Compare test statistics and critical value 7.5.1.7 Example 7.5.1.8 Decision 7.5.1.9 Example 2 7.5.1.10 Decision 7.5.2 Anderson–Darling 7.5.2.1 Test statistic 7.5.2.2 Approach 7.5.2.3 Example 7.5.2.4 Example 7.5.3 Kolmogorov–Smirnov test 7.5.3.1 Conditions 7.5.3.2 Test statistic 7.5.3.3 Approach 7.5.3.4 Example 7.5.3.5 Example 2 7.5.3.6 MATLAB 7.5.3.7 Example 1 7.5.3.8 Example 2 7.5.4 Lilliefors test 7.5.4.1 Test statistic 7.5.4.2 Approach 7.5.4.3 Example 1 7.5.4.4 Example 2 7.5.4.5 MATLAB 7.5.4.6 Example 1 7.5.4.7 Example 2 7.5.5 Jarque–Bera test 7.5.5.1 Example 7.5.5.2 Example 7.5.5.3 MATLAB 7.5.5.4 Example 1 7.5.5.5 Example 7.6 Summary Chapter 8 Parametric tests 8.1 Z test 8.1.1 One-sample z test 8.1.1.1 Example 8.1.1.2 Example 8.1.1.3 MATLAB 8.1.1.4 Example 8.1.1.5 Example 2 8.1.1.6 Example 3 8.1.1.7 Practice questions 8.1.2 Two-sample z test 8.1.2.1 Calculating the test statistic 8.1.2.2 Example 8.1.2.3 Practice questions 8.2 T test 8.2.1 One-sample t test 8.2.1.1 Example 8.2.1.2 Example 8.2.1.3 MATLAB 8.2.1.4 Example 8.2.1.5 Example 8.2.1.6 Exercise problems 8.2.2 Two-sample t test 8.2.2.1 Independent test 8.2.2.2 Summary 8.2.2.3 Example 8.2.2.4 In MATLAB 8.2.2.5 Example 8.2.2.6 Example 8.2.2.7 Exercise problems 8.2.2.8 Dependent/paired t test 8.2.2.9 Example 8.2.2.10 MATLAB 8.2.2.11 Example 8.2.2.12 Example 8.2.2.13 Exercise problems 8.2.3 The chi-square test for one variance 8.2.3.1 Steps in the chi-square test for one variance 8.3 -test 8.3.1 Steps in the F test for equality of two variances 8.3.2 Determine the p-value of the test statistic 8.3.3 Example 8.3.4 Determine the critical value of the test statistic 8.3.4.1 Finding the critical values for a right-tailed test 8.3.4.2 Finding the critical values for a two-tailed test 8.3.4.3 Finding the critical values for left-tailed test 8.3.4.4 Decision 8.3.5 F test to match two variances 8.3.5.1 Example 8.3.5.2 In MATLAB 8.3.5.3 Example: difference in BMI of males and females 8.3.5.4 Example 8.3.5.5 Exercise problems 8.3.6 Analysis of variance (ANOVA) 8.3.6.1 One-way ANOVA 8.3.6.2 Example 8.3.6.3 MATLAB 8.3.6.4 Example 8.3.6.5 Exercise problems 8.3.6.6 Two-way ANOVA 8.3.6.7 In MATLAB 8.3.6.8 Example 8.3.6.9 Example 8.3.6.10 N-way ANOVA Chapter 9 Non-parametric testing 9.1 Wilcoxon rank-sum test 9.1.1 Stating the null hypothesis 9.1.2 Calculating the test statistic 9.1.2.1 For the untied ranks example 9.1.3 Finding the p-value 9.1.3.1 The exact method 9.1.3.2 The normal approximation 9.2 Wilcoxon signed-rank test 9.2.1 One sample 9.2.1.1 Stating the hypothesis 9.2.1.2 Calculating the test statistics 9.2.1.3 Finding the p-value 9.2.2 Two sample 9.2.3 Example 9.2.4 Finding the p-value 9.2.4.1 If we want to use the exact method 9.2.4.2 Example 9.2.4.3 Example 9.2.4.4 Example 9.2.4.5 Example 9.2.4.6 If our test was left-tailed 9.2.4.7 Example 1 Example 2 9.3 Sign test 9.3.1 One sample 9.3.1.1 Stating the hypothesis 9.3.1.2 Calculating the test statistics 9.3.2 Example 1 9.3.3 Example 2 9.3.4 Example 3 9.3.5 Example 4 9.3.6 Example 5 9.3.7 Example 6 9.3.8 Computing the p-value 9.3.8.1 Exact method 9.3.8.2 Approximate method 9.3.8.3 MATLAB 9.3.9 Paired sample 9.3.9.1 Stating the hypothesis 9.3.9.2 Calculating the test statistic 9.3.9.3 Computing the p-value 9.4 Kruskal–Wallis test 9.4.1 Stating the hypotheses 9.4.1.1 Null hypothesis 9.4.1.2 Alternative hypothesis 9.4.2 Using either of the two approaches 9.4.2.1 Critical value approach 9.4.2.2 p-value approach 9.5 The Friedman test 9.5.1 Using either of the two approaches 9.5.1.1 Critical value approach 9.5.1.2 p-value approach Chapter 10 Correlation 10.1 What is correlation? 10.2 Correlation coefficient 10.2.1 Pearson correlation coefficient 10.2.2 Spearman correlation coefficient 10.2.2.1 Example 10.2.2.2 Example 10.2.2.3 Example 10.2.3 Kendall rank correlation coefficient 10.2.3.1 Example 10.2.3.2 Example 10.2.3.3 Example 10.3 Hypothesis test for correlation coefficients 10.3.1 First step: Stating the hypotheses 10.3.2 Calculating the correlation coefficient 10.3.2.1 Method 1: Using the t-test 10.3.2.2 Method 2: Using Pearson 10.3.2.3 Example 2 10.3.2.4 Example 3 10.3.2.5 Example 1 10.3.2.6 Example 10.3.2.7 Example 3 10.3.2.8 Example 1 10.3.2.9 Example 2 10.3.2.10 Example 3 10.3.2.11 Confidence interval for correlation coefficient 10.3.2.12 Example 1 10.3.2.13 Example 2 10.3.2.14 Example 3 10.4 Confidence interval of Spearman correlation coefficient 10.4.1 Example 10.4.2 Example 10.4.3 Example 10.5 Confidence interval of the Kendall correlation coefficient 10.5.1 Example 10.5.2 Example 10.5.3 Example 10.5.4 Method 1 10.5.5 Method 2 10.5.6 Let’s do Example 1 using both methods 10.5.7 Example 2 10.5.8 Example 3 10.5.9 Example 10.5.10 Example 10.5.11 Example 10.5.12 Example 10.5.13 Example 10.5.14 Example 10.5.15 Example 10.5.15.1 Test for linearity 10.5.15.2 Test for normality 10.5.15.3 Stating the hypotheses 10.5.16 Example 10.5.16.1 Stating the hypotheses 10.5.16.2 Test for linearity 10.5.16.3 Test for normality 10.5.16.4 Using the one-sample Kolmogorov–Smirnov test 10.5.17 Example 10.5.17.1 Test for linearity 10.5.17.2 Stating the hypotheses 10.5.18 Example 10.5.18.1 Stating the hypotheses 10.5.19 Example 10.5.19.1 Let’s now test for normality Chapter 11 Regression 11.1 Linear regression 11.1.1 Assumptions of linear regression regarding residuals 11.1.1.1 Let’s first talk about the plot 11.2 Estimating the regression coefficients 11.2.1 Least-squares method 11.2.2 Maximum likelihood estimation method 11.2.2.1 Using an example 11.3 Sum of squares 11.3.1 Other Sums of Squares 11.4 Coefficient of determination 11.5 Errors in the parameters of the regression line 11.6 Confidence interval for regression parameters 11.6.1 For one-sided 11.6.2 For two-sided 11.7 Inferences about the slope: The regression t test 11.7.1 State the hypotheses 11.7.2 Compute the value of the test statistic 11.7.3 Finding the p-value 11.7.3.1 Our test statistic 11.7.3.2 p-value 11.7.3.3 Our test statistic 11.7.3.4 The ANOVA table 11.8 Regression in MATLAB 11.8.1 ResidualType 11.8.1.1 Pearson 11.8.1.2 Standardized 11.8.1.3 Studentized 11.8.2 Slope coefficient 11.8.3 Intercept coefficient 11.8.4 Hypothesis test on coefficients 11.8.5 Other examples 11.8.6 Assessing the model 11.8.6.1 Test for linearity 11.8.6.2 Test for normality 11.8.6.3 Test for homoscedasticity 11.8.6.4 Test for independence 11.8.7 Assessing the model 11.9 Multiple linear regression 11.9.1 How to test multicollinearity? 11.9.1.1 Correlation matrix/correlation plot 11.9.1.2 Variation inflation factor (VIF) Detecting Multicollinearity in MATLAB 11.9.3.1 Test for linearity 11.9.3.2 Test for normality 11.9.3.3 Test for homoscedasticity 11.9.3.4 Test for independence 11.9.3.5 Test for multicollinearity 11.9.3.6 Now how do we interpret this? Matrix Approach to Multiple Linear Regression Example Errors in the Parameters of the Regression Line: Hypothesis Testing of the Significance of Regression Coefficients t – test – test coefficient of determination Root Mean Squared Error MATLAB 11.10 Linear Regression with categorical variables 11.10.1 Example with Dichotomous Predictor Variable Gender Pay Gap Comparisons with Regression Analysis Sum of Squares Errors in the Parameters of the Regression Line: Hypothesis Testing of the Significance of Regression Coefficients t - test – test coefficient of determination Root Mean Squared Error Example 2 Where Sum of Squares Errors in the Parameters of the Regression Line: Hypothesis Testing of the Significance of Regression Coefficients t – test coefficient of determination Root Mean Squared Error 11.10.2 Example with 3-level Categorical Variable Sum of Squares Errors in the Parameters of the Regression Line: Hypothesis Testing of the Significance of Regression Coefficients t - test coefficient of determination Root Mean Squared Error Calculations in MATLAB Example 1 Example 2 Example 3 11.11 Multiple Linear regression with categorical predictors 11.11.1 one continuous and one categorical Sum of Squares Errors in the Parameters of the Regression Line: Hypothesis Testing of the Significance of Regression Coefficients – test coefficient of determination Root Mean Squared Error Sum of Squares Errors in the Parameters of the Regression Line: Hypothesis Testing of the Significance of Regression Coefficients coefficient of determination Root Mean Squared Error Calculations in MATLAB 11.11.2 Two categorical predictors Sum of Squares Errors in the Parameters of the Regression Line: – test coefficient of determination Root Mean Squared Error Example Sum of Squares Errors in the Parameters of the Regression Line: Hypothesis Testing of the Significance of Regression Coefficients Lets now study the effect of Degree on the salary – test coefficient of determination Root Mean Squared Error Calculations in MATLAB 11.12 Interaction in Linear Regression 11.12.1 Calculating the Coefficient of Interaction Term 11.12.2 Interpreting interactions 11.12.3 Visualizing interactions 11.12.4 Interaction between a continuous predictor and a categorical predictor Calculations in MATLAB 11.12.5 Interaction with two binary variables 11.12.6 How do we decide whether to include the interaction term or not? Example 2 Example 3 11.13 Centering Predictors 11.13.1 Why is it important? 11.13.2 How do we do it? 11.13.3 Centering in MATLAB 11.13.4 How Centering affects the coefficients 11.13.5 Standardizing variables So how does scaling/standardizing differ from centering?  Index