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("HW23.csv")
names(pop) <- c("X1", "X2", "Y")

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

# assigns a "random" sample of 29 from the population to 'data'
data<-pop[sample(nrow(pop), 29, replace=FALSE),]

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

##       X1    X2     Y
## X1 1.000 0.384 0.539
## X2 0.384 1.000 0.172
## Y  0.539 0.172 1.000

# multiple regression model
model <- lm(Y ~ X1 + X2, data=data)
summary(model)

## 
## Call:
## lm(formula = Y ~ X1 + X2, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7796 -0.9972 -0.1482  1.0951  2.1281 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  3.47697    1.08242   3.212  0.00350 **
## X1           0.37509    0.12076   3.106  0.00454 **
## X2          -0.03296    0.14312  -0.230  0.81968   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.276 on 26 degrees of freedom
## Multiple R-squared:  0.2923, Adjusted R-squared:  0.2379 
## F-statistic: 5.369 on 2 and 26 DF,  p-value: 0.01117

# standardized beta coefficients
model_beta <- lm(scale(Y) ~ scale(X1) + scale(X2), data=data)
summary(model_beta)

## 
## Call:
## lm(formula = scale(Y) ~ scale(X1) + scale(X2), data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2178 -0.6824 -0.1014  0.7494  1.4563 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  8.934e-16  1.621e-01   0.000  1.00000   
## scale(X1)    5.551e-01  1.787e-01   3.106  0.00454 **
## scale(X2)   -4.115e-02  1.787e-01  -0.230  0.81968   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.873 on 26 degrees of freedom
## Multiple R-squared:  0.2923, Adjusted R-squared:  0.2379 
## F-statistic: 5.369 on 2 and 26 DF,  p-value: 0.01117

# calculates Pearson's r and r2
r2 <-round(summary(model)$r.squared,3)
r <-round(sqrt(r2),3)
r

## [1] 0.54

r2

## [1] 0.292