# Linear Regressions

**4.1 Linear Modeling (or Curve Fitting) with a Best-Fit Line **

**Explanation:**Khan video: Estimating the line of best-fit exercise

Khan video: Line of best fit: smoking in 1945

Khan video: Interpreting a trend line

Khan Article: Equations of trend lines: Phone data

Khan video: Slope-intercept equation from two points

Notes | Annotated

**Practice Problems:**Khan Exercise: Eyeballing the line of best fit

Khan Exercise: Estimating equations of lines of best fit, and using them to make predictions

Honors: Khan Exercise: Estimating slope of line of best fit

Honors: Khan Exercise: Interpreting slope and y-intercept of lines of best fit

Khan Exercise: Slope-intercept equation from two points

**4.2 Linear Modeling with Line of Regression (Least Square Regression)**

**Explanation:**Khan video (for the writing prompt): Predicting Linear Models - on Youtube

Spreadsheets for linear modeling

Desmos.com (click the question mark in the upper right-hand corner then Regressions for a brief tutorial). Basically, press + and select the table. Then type in the table values. Next press + and select the expression. Then type y1~mx1+b.

Google Sheets (the instructions are for after you create a table and scatterplot).

Online activity: Line of Best Fit by Illuminations (Java)

**Practice Problems:**

**4.3 Correlation: 1) finding the correlation coefficient and 2) causation vs. correlation**

**Explanation:**Khan video: Scatter plots: studying, shoe size, and test scores

Khan video: Example: Correlation coefficient intuition

Khan article: Positive and negative correlations in scatterplots

Khan video: Correlation and causality

Article: Music That Makes You Dumb

**Practice Problems:**Khan Exercise: Positive and negative linear correlations from scatter plots (nonlinear association means there is a pattern but not a line)

Khan Exercise: Describing trends in scatter plots

Khan Exercise: Correlation coefficient intuition

Annual Salary Project Google Sheet (use this file to copy and paste the annual earnings into your Google Sheet)

**4.4 Residual Plots**

**Explanation:**Khan video: Introduction to residuals and least squares regression

Khan article: Introduction to residuals

Khan video: Residual plots

**Practice Problems:**Khan exercise: Residual plots

**Review**

**Explanation:**Khan video: Calculating residual example

**Practice Problems:**Khan Exercise: Calculating and interpreting residuals (challenging)