install.packages(“rmarkdown”)

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

# loads in data for the full population
pop<-read.csv("HW19.csv", head = TRUE)
names(pop) <- c("X", "Y")

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

# assigns a "random" sample of 12 from the population to 'data'
data<-pop[sample(nrow(pop), 12, replace=FALSE),]

# use this data
data

##      X Y
## 640  5 5
## 413 12 8
## 871  9 6
## 336  5 5
## 357  7 6
## 238  7 6
## 56   5 5
## 83   8 6
## 351  7 6
## 632  9 6
## 477  9 6
## 458  6 5

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

## 
## Call:
## lm(formula = Y ~ X, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.4106 -0.3403  0.0477  0.3186  0.4957 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.12947    0.37516   8.342 8.15e-06 ***
## X            0.36457    0.04881   7.470 2.14e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3414 on 10 degrees of freedom
## Multiple R-squared:  0.848,  Adjusted R-squared:  0.8328 
## F-statistic: 55.79 on 1 and 10 DF,  p-value: 2.136e-05

# calculates Pearson's r, r2, and obt
r <- round(cor(data$X, data$Y),3)
r2 <- round(r^2,3)
n <- length(data$X)
obt <- r*(sqrt((n-2)/(1-r2)))
r

## [1] 0.921

r2

## [1] 0.848

obt

## [1] 7.470296

# creates plot
plot(data$X, data$Y, main=c(paste("Scatterplot")), xlim=c(0,10), ylim=c(0,10), xlab="X", ylab="Y")
abline(lm(Y ~ X, data=data))