Correlation and Simple Linear Regression by Dennis F Davis

This video covers a review of statistics essential to understanding the topics of correlation and simple linear regression, then goes into detail on these topics, using the scatter plot as a canvas for depicting and understanding metrics concerning correlation and regression such as covariance r, sums of squares, Correlation Coefficient r-squared, and least-squares regression. Promised Links: My 3-part Inferential Statistics series:    • Inferential Statistics Part 1: The Samplin...   Summation Notation: ‪@3-minutedatascience‬    • Sigma notation for sums | Sequences, serie...   ‪@khanacademy‬    • Sigma notation for sums | Sequences, serie...   ‪@brianmclogan‬    • what is sigma notation and how to we use it   Timestamps: 0:00 Introduction 1:39 Preview 6:48 Four Important Questions 8:21 Big Probability and Statistics Outline 10:18 Review - Levels of Measurement, Qualitative and Quantitative variable types 13:45 Review - Populations, Samples, Mean, Variance, Standard Deviation 28:41 Sum-of-Squares (SS) notation 32:19 Example: Find Mean, Variance and Standard Deviation for a small sample 35:08 Example: Try it Yourself! 35:35 Excel Functions for Mean, Variance and Standard Deviation 36:56 Introduction to Bivariate Data Analysis 40:56 Scatter Plot! 42:46 Variance as Average of Square Sizes on the Scatter Plot 44:41 The Centroid (x_bar, y_bar) 45:16 Covariance 49:23 Covariance as Average of Rectangle Sizes on the Scatter Plot 50:24 Covariance Numerical Example 51:33 Variance and Covariance Summary Chart 52:39 More Sum-of-Squares Notation 55:28 Excel Function for Covariance 56:33 Interpretation of Covariance on the Scatter Plot 1:00:30 Transforming Covariance into the Correlation Coefficient 1:03:29 The Correlation Coefficient r 1:07:29 Correlation Does Not Mean Causation! 1:09:04 Why the Correlation Coefficient Formula Works 1:11:24 Complicated-Looking Formulas Say Simple Things 1:14:23 Excel Function for Correlation Coefficient 1:15:12 Correlation Coefficient Summary Chart 1:15:23 Better Predictions Require an Improved Model 1:15:51 Finding the Best Model with Simple Linear Regression 1:17:12 Y-hat is the Predicted Value for Y based on a Model 1:18:57 Review - Equation for a Line 1:23:01 Finding the Regression Slope b 1:23:57 Finding the Regression Y-Intercept a 1:25:16 Units of Measure (Always Important!) 1:27:23 Editorial Advice 1:29:09 Example: Finding the Equation of the Least-Squares Regression Line 1:29:59 Physical Interpretation of the Regression Slope 1:31:05 Making a Prediction Using the Regression Line 1:31:31 Interpolation and Extrapolation 1:32:57 Excel Functions for Regression Slope and Y-Intercept 1:34:29 How Good is the Regression Model? 1:35:18 Sum-of-Squares Error (SSE) 1:36:55 Sum-of-Squares Regression (SSR) 1:40:48 The Coefficient of Determination r-squared (SSR/SST) 1:41:53 Correlation Coefficient vs Coefficient of Determination Summary Chart 1:44:12 Proof that the Coefficient of Determination = (Correlation Coefficient)^2 1:44:32 Introduction to Residual Analysis 1:46:56 Correlation and Regression Metrics Walk-Through 1:54:01 Complete Example Walk-Through 2:06:34 Complete Example: Try it Yourself! 2:07:51 Big Summary Chart