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MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$'], ['\$','\$']], displayMath: [['$$','$$'], ['\[','\]']], processEscapes: true, processEnvironments: true, skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'], TeX: { equationNumbers: { autoNumber: "AMS" }, extensions: ["AMSmath.js", "AMSsymbols.js"] } } }); Distributions of Random Variables Learning Outcomes Define the standardized (Z) score of a data point as the number of standard deviations it is away from the mean: $Z = \frac{x - \mu}{\sigma}$. Use the Z score if the distribution is normal: to determine the percentile score of a data point (using technology or normal probability tables) regardless of the shape of the distribution: to assess whether or not the particular observation is considered to be unusual (more than 2 standard deviations away from the mean) Depending on the shape of the distribution determine whether the median would have a negative, positive, or 0 Z score.

Chapter 5

Chapter 6

Chapter 7

MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$'], ['\$','\$']], displayMath: [['$$','$$'], ['\[','\]']], processEscapes: true, processEnvironments: true, skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'], TeX: { equationNumbers: { autoNumber: "AMS" }, extensions: ["AMSmath.js", "AMSsymbols.js"] } } }); Inference for Numerical Data Learning Outcomes Use the $t$-distribution for inference on a single mean, difference of paired (dependent) means, and difference of independent means. Explain why the $t$-distribution helps make up for the additional variability introduced by using $s$ (sample standard deviation) in calculation of the standard error, in place of $\sigma$ (population standard deviation).

Chapter 8

MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$'], ['\$','\$']], displayMath: [['$$','$$'], ['\[','\]']], processEscapes: true, processEnvironments: true, skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'], TeX: { equationNumbers: { autoNumber: "AMS" }, extensions: ["AMSmath.js", "AMSsymbols.js"] } } }); Introduction to Linear Regression Learning Outcomes Define the explanatory variable as the independent variable (predictor), and the response variable as the dependent variable (predicted). Plot the explanatory variable ($x$) on the x-axis and the response variable ($y$) on the y-axis, and fit a linear regression model $y = \beta_0 + \beta_1 x$ where $\beta_0$ is the intercept, and $\beta_1$ is the slope.

Chapter 9

MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$'], ['\$','\$']], displayMath: [['$$','$$'], ['\[','\]']], processEscapes: true, processEnvironments: true, skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'], TeX: { equationNumbers: { autoNumber: "AMS" }, extensions: ["AMSmath.js", "AMSsymbols.js"] } } }); Multiple and Logistic Regression Learning Outcomes Define the multiple linear regression model as $$\hat{y} = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \cdots + \beta_k x_k$$ where there are $k$ predictors (explanatory variables). Interpret the estimate for the intercept ($b_0$) as the expected value of $y$ when all predictors are equal to 0, on average.

Bayesian

Bayesian Analysis Supplemental Readings Chapter 17 of Learning Statistics with R (Navarro, version 0.6) Fitting a Model by Maximum Likelihood (Collier, 2013). Kruschke’s website for Doing Bayesian Data Analysis Kruschke’s blog Andrew Gelman’s blog - Posts about bayesian statistics Videos Rasmus Bååth’s Introduction to Bayesian Data Analysis Video Series John Kruschke’s Video Series Bayesian Methods Interpret Data Better Bayesian Estimation Supersedes the t Test

Chapters

Chapter 1

Chapter 2