# Homework Key for Week 4

# 1. Read in and inspect the data.

d = dfReadDat('Salary.dat')
varDescribe(d)
summary(d)
View(d)

# 2. Is the mean faculty salary significantly greater (or smaller) than $50,000/year? 
# Report the corresponding F-statistic, df and p-value.

d$sal50 = d$SALARY - 50000
m1 = lm(sal50 ~ 1, data=d)
modelSummary(m1, t=F)
# It is significantly greater, F(1,61) = 15.26, df = 61, p < 0.001.
# Most researchers would actually report t in this case, since
# this is a one-sample t-test.

# 3. Fit a linear model predicting salary from number of publications. Test if the number of 
# publications significantly predicts salary

m2 = lm(SALARY ~ 1 + PUBS, data=d)
modelSummary(m2, t=F)
confint(m2)
# For every publication, professor salary increases $351, on average, F(1,60) = 20.66, df = 60,
# p < 0.001. Confidence interval [196.44, 505.16]

# 4. Report a variance-based indicator of effect size, along with its interpretation.

modelEffectSizes(m2)
# partial eta squared = 0.256. Number of publications explains 25.6% of the variance in salary.

# 5. To better understand this effect, you'll now calculate some predicted salaries based on 
# number of publications.
# a. 5 publications?

48439.09 + 350.8*5
# $50139.09

# b. 15 publications?

48439.09 + 350.08*15
# 53690.29

## This could also be done by recentering the publication variable first around 5 and then
## around 15.

# 6. Create a scatterplot for Salary by Publications. Include the regression line of the model 
# as well as lines representing the standard error of the point estimate. Paste this plot into 
# your Word document.

pY1 = data.frame(PUBS=seq(1,69,length=62))
pY1 = modelPredictions(m2, pY1)
plot1 = ggplot(d, aes(x = PUBS, y = SALARY))
plot1
plot1 = plot1 + geom_point(data=d, aes(x = PUBS, y = SALARY), color = 'black')
plot1
plot1 = plot1 + geom_smooth(aes(ymin=CILo, ymax=CIHi, x=PUBS, y=Predicted), data=pY1, stat='identity', color='red')
plot1
plot1 = plot1 + theme_bw(base_size = 14) + labs(x = 'Number of publications', y = 'Salary')
plot1


# 7.

plot1 = plot1 + scale_x_continuous(breaks = seq(0, 70, 10)) + theme(panel.grid.major = element_blank())
plot1 # changed x axis ticks and removed (some) gridlines

# Fun packages with Mitch: To save myself some time doing the theme things, I often use the following package:
install.packages('cowplot')
library(cowplot)
??cowplot
plot1 = ggplot(d, aes(x = PUBS, y = SALARY)) + geom_point(data=d, aes(x = PUBS, y = SALARY), color = 'black') + 
  geom_smooth(aes(ymin=CILo, ymax=CIHi, x=PUBS, y=Predicted), data=pY1, stat='identity', color='red') + 
  labs(x = 'Number of publications', y = 'Salary') + scale_x_continuous(breaks = seq(0, 70, 10))
plot1