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("HW22.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 10 from the population to 'data'
data<-pop[sample(nrow(pop), 10, replace=FALSE),]

# use this data
data

##      X Y
## 640  6 5
## 413  8 6
## 871  8 6
## 336  7 6
## 357  7 6
## 238 10 7
## 56   9 6
## 83   8 6
## 351  8 6
## 632  8 6

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

## 
## Call:
## lm(formula = Y ~ X, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.4037 -0.0367 -0.0367  0.1628  0.3303 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  3.10092    0.62249   4.982  0.00108 **
## X            0.36697    0.07812   4.698  0.00155 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2579 on 8 degrees of freedom
## Multiple R-squared:  0.7339, Adjusted R-squared:  0.7007 
## F-statistic: 22.07 on 1 and 8 DF,  p-value: 0.001546

# calculates Pearson's r and r2
r <- round(cor(data$X, data$Y),3)
r2 <- round(r^2,3)
r

## [1] 0.857

r2

## [1] 0.734

# 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))

# calculates predicted values and residuals
data$Y_pred <-round(predict(model),2)
data$resid <-round(residuals(model),2)

data

##      X Y Y_pred resid
## 640  6 5   5.30 -0.30
## 413  8 6   6.04 -0.04
## 871  8 6   6.04 -0.04
## 336  7 6   5.67  0.33
## 357  7 6   5.67  0.33
## 238 10 7   6.77  0.23
## 56   9 6   6.40 -0.40
## 83   8 6   6.04 -0.04
## 351  8 6   6.04 -0.04
## 632  8 6   6.04 -0.04

# creates residual plot
plot(data$X, data$resid, main=c(paste("Residual Plot")), xlab="X", ylab="Y-Y'")
abline(0,0)