Linear regression package result vs econometric result mismatch

Question

x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)
y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)
relation <- lm(y~x) 
print(relation)
beta=solve(t(x)%*%x)%*%(t(x)%*%y)
print(beta)

---

Result from lm coeff = 0.6746

Result from beta econometrics = 0.4287

Why?

Answer 1

The results differ because you didn't include the intercept:

lm(y ~ 0 + x)
## 
## Call:
## lm(formula = y ~ 0 + x)
## 
## Coefficients:
##      x  
## 0.4287 

or

X <- cbind(Intercept = 1, x)
solve(t(X) %*% X) %*% (t(X) %*% y)
##                  [,1]
## Intercept -38.4550871
## x           0.6746104 

This has nothing to do with econometrics and I doubt any econometrics handbook or course recommends not including intercept as it is a bad practice.