# Cook's Distance

I have a problem with calculating Cook Distance (I'm trying to understand it).

Ok so here is the task and my 'solution'. I'm asking for comment, is it ok, or what do I wrong.

We have simple linear model for $$10$$ observations $$Y =b_0+ b_1X_1 + b_2X_2 + b_3X_3$$, where $$X_1$$ and $$X_2$$ are numbers and $$X_3$$ can be $$Z$$ or $$D$$.

And the result of the model is:

(intercept) $$18,1422$$

$$X_1$$: $$-0,6349$$

$$X_2$$: $$-0,1577$$

$$X_3 Z$$: $$-0,3828$$

We also know $$RSS=0,81632$$ and leverages $$h_{ii} = (0,68894\; 0,45208\; 0,53916\; 0,26537\; 0,32897\; 0,34334\; 0,28986\; 0,23839\; 0,58853\; 0,26537)$$

My task is to calculate Cook's Distance for first observation : $$Y_1=6$$ and $$X_1=12$$, $$X_2=25$$, $$X_3=Z$$.

So, I've started from searching the formula for Cook's Distance: $$D_1=\frac{(y_1-\hat{y_1})^2}{k \cdot MSE}\cdot \frac{h_{11}}{(1-h_{11})^2}$$.

Then I calculate $$\hat{y_1}=18,1422 -0,6349 \cdot 12 -0,1577 \cdot 25 -0,3828 = 6,1981$$ Next $$MSE=\frac{RSS}{10}=0,081632$$

We have $$k=3$$ and $$h_{11}=0,68894$$.

Using the formula above we have finally: $$D_1=1,1408$$

My questions are:

1. Is it a good solution?

2. Can Cook Distance be greater than $$1$$?

$$k$$ will be $$4$$ not $$3$$, number of parameters in the full model. $$Y1$$ estimate should be obtained using model fitted ignoring the first observation as you are interested in finding the influence of the first observation.