Question

X1	Y1	Studentized Deleted Residual (Round your answers to two decimal places)
1	5	???
2	9	???
3	7	???
4	13	???
5	16	???

At the 0.05 level of significance, can any of these observations be classified as an outlier? Explain. (Select all that apply.)

Observation x_i = 1 can be classified as an outlier since it has a large studentized deleted residual (greater than t_0.025 or less than −t_0.025).
Observation x_i = 2 can be classified as an outlier since it has a large studentized deleted residual (greater than t_0.025 or less than −t_0.025)
Observation x_i = 3 can be classified as an outlier since it has a large studentized deleted residual (greater than t_0.025 or less than −t_0.025).
Observation x_i = 4 can be classified as an outlier since it has a large studentized deleted residual (greater than t_0.025 or less than −t_0.025).
Observation x_i = 5 can be classified as an outlier since it has a large studentized deleted residual (greater than t_0.025 or less than −t_0.025)
None of the observations can be classified as outliers since they do not have large studentized deleted residuals (greater than t_0.025 or less than −t_0.025).

Answer 1

Above is the R screenshot. On right side is output and on left side is R code.

We can see at 4 degrees of freedom

and

Standardised residual are

1 2 3 4 5
0.1555428 0.9406342 -1.6497800 0.2351585 0.6221710

If an observation has a studentized residual that is larger than 3 (in absolute value) we can call it an outlier.

None of the observations can be classified as outliers since they do not have large studentized deleted residuals