Interpretation Of Fitted Models

Question 1

Point prediction? (SLRM) and dist?

Answer 1

For an unknown (not observed) response at some x_0

Question 2

How to form prediction interval (SLRM)

Answer 2

-find dist of μ^^_0 - Y_0
-Standardize μ^^_0 - Y_0 by replacing σ^2 by its estimator to get

a=(1/n + (x_0 - x^-)^2/S_xx)

Question 3

(1-α)100% PI for Y_0 in SLRM is?

Answer 3

Question 4

Compare PI to CI for mean response μ_0

Answer 4

PI is wider than CI because to predict a new observation rather than a mean, we need to add variability of additional random error ε_0

Question 5

Only make predictions for values

Answer 5

Within range of data

Question 6

To predict a new observation we need to take into account

Answer 6

It’s expectations and also a possible new random error

Question 7

Point estimator of new observation (below) is (general regression)? And dist?

Answer 7

Question 8

(1-α)100% PI for Y_0 is? (General regression) vector form

Answer 8

Question 9

How to write quadratic regression model in vectors

Answer 9

Question 10

How to compare quadratic regression model w SLRM

Answer 10

-fit Y_i = β_0 + β_1*x_i + β_11 * (x_i)^2 + ε_i
-test H_0: β_11 = 0 against H_1: β_11 != 0
-reject null if quad gives statistically significant better fit

Question 11

If polynomial model has some higher order terms that are large

Answer 11

Centre x by subtracting it’s mean, eg:

Question 12

If model is polynomial, which terms do you consider removing first?

Answer 12

Higher order, given that the Lower order is there, eg
-if x_2,i and x^2_2,i are both there, begin w x^2_2,i

Question 13

Linear form of polynomial regression models

Answer 13

Question 14

Sequential sum of squares

Answer 14

SS_R - SS_R (without the new variable)

Remember SS_R
Is regression sum of squares (sum((predictions-mean)^2))

Question 15

How to use sequential sum of squares

Answer 15

Taking SS_R and difference from previous SS_R when adding variables:
If difference is relatively small. Don’t need that variable