This activity requires the use of a statistical computer package capable of fitting multiple regression models. Background: The given data on y, x₁, x₂, x₃, and x₄ were generated using a computer package capable of producing random observations from any specified normal distribution. Because the data were generated at random, there is no reason to believe that y is related to any of the proposed predictor variables x₁, x₂, x₃, and x₄.

1. Construct four scatterplots—one of y versus each of x₁, x₂, x₃, and x₄. Do the scatterplots look the way you expected based on the way the data were generated? Explain.

2. Fit each of the following regression models:

i. y with x₁

ii. y with x₁ and x₂

iii. y with x₁ and x₂ and x₃

iv. y with x₁ and x₂ and x₃ and x₄

3. Make a table that gives the R², the adjusted R², and s_e values for each of the models fit in Step 2. Write a few sentences describing what happens to each of these three quantities as additional variables are added to the multiple regression model.

4. Given the manner in which these data were generated, what is the implication of what you observed in Step 3? What does this suggest about the relationship between number of predictors and sample size?

Transcribed Image Text:

у 20.5 20.1 20.0 21.7 20.7 X1 18.6 23.9 20.9 18.7 21.1 Х2 22.0 19.1 20.7 18.1 21.7 X3 17.1 21.1 19.4 20.9 23.7 ХА 18.5 21.3 20.6 18.1 17.0