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("HW20.csv")
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  9 6
## 413  9 6
## 871  8 6
## 336  5 5
## 357  8 6
## 238  7 6
## 56  10 7
## 83   9 6
## 351  9 6
## 632 13 8
## 477  8 6
## 458 11 7

# sum of squares for Y
SSY <- sum((data$Y-mean(data$Y))^2)
SSY

## [1] 6.25

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

## 
## Call:
## lm(formula = Y ~ X, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.3092 -0.3092  0.0458  0.1508  0.4008 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.11450    0.37405   8.327 8.28e-06 ***
## X            0.35496    0.04139   8.576 6.37e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2735 on 10 degrees of freedom
## Multiple R-squared:  0.8803, Adjusted R-squared:  0.8683 
## F-statistic: 73.55 on 1 and 10 DF,  p-value: 6.373e-06

# ANOVA
anova<-anova(model)
anova

## Analysis of Variance Table
## 
## Response: Y
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## X          1 5.5019  5.5019  73.546 6.373e-06 ***
## Residuals 10 0.7481  0.0748                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# calculates Pearson's r, r2, and the standard error of the estimate
r <- round(cor(data$X, data$Y),3)
r2 <- round(r^2,3)
n <- length(data$X)
SEE <-sqrt((anova$'Sum Sq'[2])/(n-2))

r

## [1] 0.938

r2

## [1] 0.88

SEE

## [1] 0.2735126