You have 2 explanatory variables x1 and x2 below, and a response variable y. Please fit the least square hyperplane.

x1=c(9.9, 4.2, 2.7, 4.2, 1.6, 2.5, 0.8, 1.3, 0.2, 4.6, 0.2, 0.5, 4.8, 1.5, 4.6, 3.8, 2.3, 2.4, 0.1, 1.4)

x2=c(10.2, 3.8, 3.1, 1.6, 1.3, 3.4, 4.4, 2.2, 4.6, 5.2, 2, 4.1, 5.5, 2, 4.4, 2, 3.8, 3.6, 1.9, 5.1)

and

y=c(53.4, 22.4, 16.6, 18.9, 9.6, 16.3, 14.9, 10.6, 12.8, 28.1, 8.3, 12.8, 28.6, 12.3, 25.1, 13.8, 17.9, 17.3, 6.4, 17.5)

Part a)

The slope ofx

1

x1for the least square hyperplane is

^

1

^1=

Part b)

The value of largest absolute residual is:

Part c)

Based on Cook's distances or the dfit statistics, from ls.diag() applied to an lm object, does the observation with the largest absolute residual correspond to an influential observation? (Enter either Yes or No)

Part d)

Check the output of Cook's distances or the dfit statistics, and check on how your largest absolute residual compares with the other residuals. Then determine the best answers below on interpretations of influential observations.

Possibly more than one item is correct.

A.Influential observations should be deleted

B.Influential observations sometimes are in the extremes of the space of explanatory variables

C.An influential observation need not have an extreme residual

D.Influential observations have heavy influence on some

^

^

E.In general, influential observations are extreme residuals (outliers)

F.The number of influential observations can be 0,1,2,..., or n-p-1, where p is the number of explanatory variables

G.None of the above

I don't know the last multiple question.