Applied statistics (ESB: RISK)

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Multiple linear regression

Literature

[WMMY] Chapter 12.1, 12.2, 12.4, 12.5 until p.476m, 12.6, 12.8

Lecture material

This lecture as: slideshow (html), Rmarkdown (Rmd), notes (pdf).

The entire module: notes (pdf).

Exercises

Consider the following prediction equation without interaction: ŷ = 2 + 0.4x₁ + 0.7x₂. What does the equation for the predicted response look like when x₁ = 1? What does the equation for the predicted response look like when x₁ = 5?
Consider the following prediction equation with interaction: ŷ = 2 + 0.4x₁ + 0.7x₂ − 0.1x₁x₂. What does the equation for the predicted response look like when x₁ = 1? What does the equation for the predicted response look like when x₁ = 5? Explain the difference between the models in 1. and 2.
For this exercise we use data from [WMMY] Exercise 12.5. You find the exercise in the Rmarkdown file Exercise_12-5.Rmd.
Answer the questions below using the Rmarkdown file GNP.Rmd.
- In this exercise we consider a dataset containing macro economical numbers for USA collected in the years 1947 to 1962. The dataset contains 7 variables:
  1. GNP.deflator: GNP implicit price deflator
  2. GNP: Gross National Product
  3. Unemployed: Number of people that are unemployed
  4. Armed.Forces: Number of staff in the armed forces
  5. Population: Population size (age >=14)
  6. Year: Year
  7. Employed: Number of people that are employed
- Make a multiple linear regression model with ‘GNP’ as response and ‘Population’ as explanatory variable.
- What is the interpretation of the estimates? Is the population size significant for GNP?
- Repeat the analysis above, but now with ‘Year’ as explanatory variable. Is time significant?
- Repeat the analysis above, but now with both ‘Population’ and ‘Year’ as explanatory variables. Conclusion?
- Make pairwise scatter plots (e.g. ggscatmat from the GGally package) of GNP, Population and Year
  - Does the plot explain your results?