# Title: Associative tests in R: Correlation to multivariate regression
# Author: Jason C. Rodin
# Affiliation: 
#     Department of Psychology, Sociology, and Social Work
#     West Texas A&M University
#
'THANK YOU to the following for supporting student travel and this event: 
    College of Education and Social Sciences
    Department of Psychology, Sociology, and Social Work
    Dr. Lisa Garza'
#
# Load the necessary packages ----
library(apaTables) # Useful for near-APA output
library(broom)     # Useful for converting statistical objects into Tidy Tibbles
library(corrplot)  # Creates visual plots of correlation matrices
library(dplyr)     # Useful for data manipulation/wrangling
library(ggfortify) # Allows ggplot2 to handle some popular packages
library(ggplot2)   # Useful for creating graphs
library(ggplotgui) # Allows GUI interface with ggplot
library(gvlma)     # Useful for global validation of regression assumptions
library(readr)     # Used to import the .csv

# Import the .csv titled "gradedata_2020" ----
gradedata_2020 <- as_tibble(read_csv("gradedata_2020.csv"))


# Next, we are going to practice selecting only 
# the variables that we will need for this example.
gradedata_tibble <- select(gradedata_2020, minStudy, SAT, FinalExam)

# Helpful functions for getting started ----

# summary() provides a descriptive summary for each element of the tibble
summary(gradedata_tibble)

# View() displays the data in a form similar to many spreadsheets
View(gradedata_tibble)

# head() previews the first 6 observations by default
head(gradedata_tibble)

# tail() previews the last 6 observations by default
tail(gradedata_tibble)

# class() provides the class of our tibble
class(gradedata_tibble)

# str() lets us look at the structure of our data
str(gradedata_tibble)


# Create a linear model ----
regression_model <- lm(
  formula = FinalExam ~ minStudy + SAT,
  data = gradedata_tibble
)

# Assumption testing ----
gvlma.lm(regression_model)

# Check plots (Make sure margins are wide enough for this step)
plot(gvlma(regression_model), onepage = FALSE)

# We could also have used
autoplot(regression_model)+theme_classic()

# Check the mean of the residuals
round(<INSERT FUNCTION 'mean'>(regression_model$residuals),3)

# Check the histogram of the residuals
<INSERT FUNCTION 'hist'>(regression_model$residuals)

# To augment the regression_model to a Tidy Tibble
tidy_regression_metrics <- 
  <INSERT FUNCTION 'round'>(augment(regression_model), 3)

# To view a summary of the tidy_regression_metrics
summary(tidy_regression_metrics)

# Creating scatterplots
ggplot_shiny(gradedata_tibble)

# Scatterplot 1
scatterplot1 <- ggplot(
  gradedata_tibble, 
  aes(x = minStudy, y = FinalExam)) +
  geom_point() +
  labs(x = 'Minutes spent studying', y = 'Final exam grade') +
  ggtitle('Scatterplot of minutes studying and final exam grade') +
  theme_classic()+ 
  geom_smooth(method='lm')

scatterplot1

# Scatterplot 2
scatterplot2 <- <INSERT FUNCTION 'ggplot'>(
  gradedata_tibble, 
  aes(x = SAT, y = FinalExam)) +
  geom_point() +
  labs(x = 'SAT', y = 'Final exam grade') +
  ggtitle('Scatterplot of SAT score and final exam grade') +
  theme_classic()+ 
  geom_smooth(method='lm')

scatterplot2

# Correlation coefficients ----

# To create a correlation coefficient matrix
correlation_coefficients <-
  round(<INSERT FUNCTION 'cor'>(gradedata_tibble, method = "pearson"),3)

correlation_coefficients

# To export those results in near-APA
apa.cor.table(
  data = gradedata_tibble,
  filename = "Correlation Matrix Example.doc"
)

# To visualize the correlation matrix 
corrplot(correlation_coefficients, method = "circle",
         addCoef.col = TRUE)

# Regression coefficients ----

# summary of the regression_model
<INSERT FUNCTION 'summary'>(regression_model)

# To examine the regression coefficients and store 
# the results as the object "regression_coefficients"
regression_coefficients <- 
  tidy(regression_model)

regression_coefficients  

# To export the results in near-APA
apa.reg.table(
  data = regression_model,
  filename = "Multiple Regression Example.doc",
  prop.var.conf.level = .95)

# Alternatively, we could bootstrap the results
apa.reg.boot.table(
  data = regression_model,
  filename = "Multiple Regression Bootstrapped Example.doc",
  number.samples = 1000)

# Useful functions for regression ----


# model regression coefficients
coefficients(regression_model) 

# CIs for model parameters
confint(regression_model, level=0.95)

# predicted values
fitted(regression_model) 

# residuals
residuals(regression_model) 

# anova table
anova(regression_model)

# covariance matrix for model parameters
vcov(regression_model) 

# regression diagnostics
influence(regression_model)