From Statistics for Engineering
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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 notes 2015