Learning outcomes
- Understand the difference between correlation and covariance.
- What the objective function of least squares does
- Understand and use an analysis of variance table
- Calculate and interpret the confidence intervals from a least squares model
- Know about the assumptions required to interpret least squares model coefficients
- Use the prediction error range from the model
- Identify outlier points and classify them
- Use the linear model when there are multiple predictor variables (this is what we are building up towards; we will use this extensively in the next topic)
Extended readings/practice
- Run the code below to see how to build and use a linear model in R, but see step 16 and onwards in the R tutorial as well.
- Try some practice problems.
- Describe a linear regression model you have made for a lab report.
- What was the \(R^2\) value?
- How did you calculate the regression model values?
- Use the same data from your report and instead calculate the standard error, \(S_E\). How do you interpret that \(S_E\) value now?
- Do the YouTube challenge: find a video on YouTube that explains the central limit theorem, or the confidence interval, or least squares in a way that is different to explained in class (hopefully you find better explanations than mine). Share the link with a friend in your class.
- Does eating chocolate lead to winning a Nobel prize?
Resources
Class videos from prior years
Videos from 2015
- Overview of this module [02:59]
- Covariance and correlation [09:46]
- Why least squares, and some other alternatives [covered in class]
- Some of the math behind the LS model [09:44]
- Understanding the analysis of variance (ANOVA) [11:58]
- Interpretation of standard error [covered in class]
- Assumptions to derive LS confidence intervals [05:45]
- Confidence intervals interpreted and used in 3 LS examples [11:54]
- Prediction intervals from the least squares model [04:24]
- Checking for violations of the least squares assumptions (1 of 2) [07:27]
- Checking for violations of the least squares assumptions (2 of 2) [11:46]
- Introducing multiple linear regression - why we need to use it [2:59]
- MLR - the matrix equation form and an example [11:25]
- Interpreting the MLR model coefficients and confidence intervals [04:58]
- Integer variables in the multiple linear regression model [09:51]
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| Covered in class | No video | Script
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| Covered in class | No video | Script
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Videos from 2014
See the webpage from 2014
Videos from 2013
See the webpage from 2013
Class notes 2015