STOR 455 Study Guide - Final Guide: Tachykinin Receptor 1, Mean Squared Error, Prediction Interval
18 May 2018
School
Department
Course
Professor
MLR
e = yi – Yihat (fitted values of model)
first column of X is 1
mean sq
error
Residual Analysis: Plot e against Xi, Yi hat, and see quantile plot of e
Confidence
/Prediction interval
in MLR
(muy CI,
Yhat, Pred Int)
ANOVA IN MLR
Total Sum of Squares df = n-1,
Total mean sq for Y = MSY = SSY/n -1 ; n – 1 = df
Sum of Squared Errors = SSE = listed above ; n-k-1 df
Mean sq error = MSE = SSE / n-k-1
Sum of sq due to regression = df = k
Mean sq due to regression = MSR = SSR / (n-1)-(n-k-1)
F statistic = MSR/MSE
COMPARING TWO MODELS
P value = 1-pf(21.721,4,15) → If H0 is true, we would expect to choose
20 students at random, we would get an F value this large or large
4.225*10^-6 times which is really low so we reject the null
MODEL SELECTION
look at adj R^2 instead bc any time we add a
variable R^2 goes up. Adj R^2 penalizes R^2
MODEL SELECTION
Top Down – Check full model, and remove the least helpful predictor 1
by 1 until adj R^2 decreases
Bottom up – start with one variable and add other variables 1 by 1
(may arrive at different models so use p values when add/del variable)
P Value Approach – set a significance level and compare the p values
to this significance level for backward elim and forward selection
ILL CONDITIONING
A matrix is ill conditioned if small errors lead to big changes
Ri2 a e foud Xi ~ X1 +…+
Xi–1 + Xi+1 +Xn
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Top down check full model, and remove the least helpful predictor 1 by 1 until adj r^2 decreases. Bottom up start with one variable and add other variables 1 by 1 (may arrive at different models so use p values when add/del variable) P value approach set a significance level and compare the p values to this significance level for backward elim and forward selection. Mlr e = yi yihat (fitted values of model) first column of x is 1 mean sq error. Residual analysis: plot e against xi, yi hat, and see quantile plot of e. Total mean sq for y = msy = ssy/n -1 ; n 1 = df. Sum of squared errors = sse = listed above ; n-k-1 df. Mean sq error = mse = sse / n-k-1. Mean sq due to regression = msr = ssr / (n-1)-(n-k-1) A matrix is ill conditioned if small errors lead to big changes.
