126_HW4

n <- 100
x <- seq(0,1,length=n)
y <- vector(length=100)
e <- rnorm(100)
y= 1+ 2*x +e
model=lm(y~x)
summary(model)

## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.10132 -0.60480  0.05776  0.58731  2.48614 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.9905     0.1854   5.342 5.97e-07 ***
## x             2.2220     0.3203   6.937 4.34e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.934 on 98 degrees of freedom
## Multiple R-squared:  0.3293, Adjusted R-squared:  0.3225 
## F-statistic: 48.12 on 1 and 98 DF,  p-value: 4.341e-10

z=cbind(rep(1,100),x)
b <- solve(t(z)%*%z)%*%t(z)%*%y
b

##        [,1]
##   0.9904802
## x 2.2219540