Least squares modelling

From Statistics for Engineering
Jump to navigation Jump to search

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