install.packages(“rmarkdown”) install.packages(“ppcor”)

# sets wd to the path on my computer; 
setwd("C:\\Users\\hmon1\\Desktop\\10C Homework\\") #this is where you downloaded the HW1.csv file

library("ppcor")

## Warning: package 'ppcor' was built under R version 3.5.3

## Loading required package: MASS

# loads in data for the full population
pop<-read.csv("HW24.csv")
names(pop) <- c("X", "Z", "Y")

# sets the seed for the random number generator
set.seed(48183130)  #use your student ID instead of 12345678

# assigns a "random" sample of 10 from the population to 'data'
data<-pop[sample(nrow(pop), 10, replace=FALSE),]

# use this matrix
matrix<-round(cor(data),3)
matrix

##        X      Z      Y
## X  1.000 -0.137  0.784
## Z -0.137  1.000 -0.403
## Y  0.784 -0.403  1.000

# r_yx.z
pcor.test(data$Y, data$X, data$Z)

##    estimate     p.value statistic  n gp  Method
## 1 0.8043334 0.008957861  3.581528 10  1 pearson

# r_y(x.z)
spcor.test(data$Y, data$X, data$Z)

##    estimate    p.value statistic  n gp  Method
## 1 0.7361596 0.02372719  2.877766 10  1 pearson

# r_yz.x
pcor.test(data$Y, data$Z, data$X)

##     estimate   p.value statistic  n gp  Method
## 1 -0.4807126 0.1902264 -1.450425 10  1 pearson

# r_y(z.x)
spcor.test(data$Y, data$Z, data$X)

##     estimate   p.value  statistic  n gp  Method
## 1 -0.2981253 0.4358669 -0.8263419 10  1 pearson

# regression
model <- lm(Y ~ X + Z, data=data)
summary(model)

## 
## Call:
## lm(formula = Y ~ X + Z, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.63393 -0.32462 -0.05817  0.53851  1.53208 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   3.5272     2.1061   1.675  0.13790   
## X             0.5830     0.1628   3.582  0.00896 **
## Z            -0.2563     0.1767  -1.450  0.19023   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9728 on 7 degrees of freedom
## Multiple R-squared:  0.7043, Adjusted R-squared:  0.6198 
## F-statistic: 8.335 on 2 and 7 DF,  p-value: 0.01407

# calculates Pearson's r and r2
r2 <-round(summary(lm(Y ~ X + Z, data=data))$r.squared,3)
r2

## [1] 0.704