Question

Data for two variables, x and y, follow.

xi	22	24	25	28	41
yi	12	23	31	36	69

a. Develop the estimated regression equation for these data (to 2 decimals). Enter negative value as negative number.

y=-43.71+2.78x

b. Compute the standardized residuals for these data (to 2 decimals). Enter negative value as negative number.

xi	yi	Standardized Residual
22	12
24	23	-0.02
25	31	1.31
28	36
41	69

c. Compute the leverage values for these data (to 2 decimals).

xi	yi	hi
22	12
24	23
25	31
28	36
41	69

With only five points it is difficult to determine if the model assumptions are violated.

d. Compute Cook’s distance measure for these data (to 2 decimals).

xi	yi	di
22	12
24	23
25	31
28	36
41	69

How many observations influential?

We conclude that the ____ th observation is influential.

Answer 1

a.

b. -1.51, -0.02, 1.30, 0.44, -1.18

c. 0.36, 0.27, 0.24, 0.20, 0.93

d.  26.71, 0.00, 10.97 , 1.00, 366.70

3 observations are influencial (since if D>1 we consider this observation is influential)

First, 3rd and 5th observations are influential.

R code:

x=c(22,24,25,28,41)
y=c(12,23,31,36,69)
Model=lm(y~x)
Model #a
round(rstandard(Model),2)#b
X=cbind(rep(1,5),x)
H=X%*%solve(t(X)%*%X)%*%t(X)
h=round(diag(H),2)
h#c
e=y-(-43.713+2.783*x)
r=1:5*0
D=r
for(i in 1:5)
{
r[i]=e[i]/sqrt(1-h[i])
D[i]=(r[i])^2*(h[i]/(1-h[i]))
}
round(D,2) #d