M

In MASS package in R, I can do weighted linear regression by passing a weight parameter to `lm`. It can be seen that the model with weights is different from the one without weights.

Code:

```
# with weights
> model = lm( y ~ X - 1, weights = w)
> model$coeff
X(Intercept) XSepal.Length XSepal.Width XPetal.Length XPetal.Width
-2.1135159 -0.1890203 1.8198141 -1.1771699 2.2840825
# without weights
> model = lm( y ~ X - 1)
> model$coeff
X(Intercept) XSepal.Length XSepal.Width XPetal.Length XPetal.Width
-5.23869771 0.09802533 2.16742901 -1.07331102 2.40425352
```

Code:

```
# with weights
> model = lm.ridge(y ~ X - 1, lambda=lmd, weights = w)
> model
X(Intercept) XSepal.Length XSepal.Width XPetal.Length XPetal.Width
-5.17253104 0.08770593 2.15946954 -1.06284572 2.38714738
# without weights
> model = lm.ridge(y ~ X - 1, lambda=lmd, weights = w)
> model
X(Intercept) XSepal.Length XSepal.Width XPetal.Length XPetal.Width
-5.17253104 0.08770593 2.15946954 -1.06284572 2.38714738
```