Linear Models and Multiple Regression

UNG MATH 3350 (online)

I. Initialization Block

Initializing RStudio

The data set we will use primarily is Data3350 which was produced in 2015 during an undergraduate research project about personality and humor. The VarsData3350 PDF file has descriptions of each variable in the Data3350 file. Both are available for download in D2L. Be sure to put the Data3350 in your R folder in Documents, and make sure your working directory is set the same way (Session menu). The code block below uses the library function to ensure that the Mosaic package is loaded and will import the data frame used in this module: Data3350.

library(mosaic)
library(readxl)
Data3350 = read_excel("Data3350.xlsx")

II. Exercises

1. Add the non-numeric variable biological Sex to the Thrill-seeking model above to test the stereotype of males being more adventurous than females. The stats notation for the model is \[\text{Thrill} \sim \text{Anx} + \text{Narc} + \text{Play} + \text{Sex}\] Is the variable Sex a significant predictor? Does it add anything to the model? Did the diagnostic plots change in any significant way?

\[\text{Thrill} \sim \text{Anx} + \text{Narc} + \text{Play} + \text{Sex}\]

2. Using the HSAG variable from the Data3350 data frame, build a linear model for Aggressive Humor using the predictors Narcissism and Self-Defeating Humor Style: \[\text{HSAG} \sim \text{Narc} + \text{HSSD}\] Evaluate and analyze your model including all diagnostic plots.

3. Add the Eating Attitudes variable Eat as the third predictor in your model for HSAG:\[\text{HSAG} \sim \text{Narc} + \text{HSSD} + \text{Eat}\] Evaluate and analyze your model including all diagnostic plots, and compare your three-predictor model with your results from the two-predictor model. Is the correlation between Eat and HSAG positive or negative? How can you tell from the model summary statistics output? If higher scores on the Eat variable indicate higher levels of being calorie conscious, knowing the fat content of food items and thinking about burning calories when working out, does this relationship between Eat and HSAG make sense?

4. Using the OCD variable from the Data3350 data frame, build a two-predictor linear model using Perf and TypeA as predictors: \[\text{OCD} \sim \text{Perf} + \text{TypeA}\] Evaluate and analyze your model including all diagnostic plots.

5. Add Anx as the third predictor in your model for OCD: \[\text{OCD} \sim \text{Perf} + \text{TypeA}+ \text{Anx}\] Evaluate and analyze your model including all diagnostic plots, and compare your three-predictor model with your results from the two-predictor model.

III. Code Blocks

mod = lm(Anx ~ Opt, data = Data3350)
summary(mod)

plot(mod)

plot(mod, which = c(1,2))

summary(mod)

mod2 = lm(Anx ~ Opt + Neuro, data = Data3350)
summary(mod2)

plot(mod2, which = c(1,2))

mod3 = lm(Anx ~ Opt + Neuro + SE, data = Data3350)
summary(mod3)

plot(mod3, which = c(1,2))

mod4 = lm(Thrill ~ Anx + Narc + Play + CHS + Opt, data = Data3350)
summary(mod4)

plot(mod4, which = c(1,2))

mod5 = lm(Thrill ~ Anx + Narc + Play + Opt, data = Data3350)
summary(mod5)

plot(mod5, which = c(1,2))

mod6 = lm(Thrill ~ Anx + Narc + Play, data = Data3350)
summary(mod6)

plot(mod6, which = c(1,2))