Squares and Black Boxes

Returns to AI?

• New Yorker

The squares criterion is broadly applied.

• Principal components derives the variable that accounts for the maximum variation in the collection of variables under study.

• Regression trees split continuous variables into groupings with minimal variation in the outcomes.

• Clustering identifies variance reducing groups in multidimensional data.

Each of these falls under the general guise of machine learning along with the principle of training and testing on data.

A link to the slides for the day.

Slides

Slides-old

The most important piece of code.

load(url("https://github.com/robertwwalker/DADMStuff/raw/master/RegressionExamples.RData"))
library(radiant)

Loading required package: radiant.data

Loading required package: magrittr

Loading required package: ggplot2

Loading required package: lubridate

Attaching package: 'lubridate'

The following objects are masked from 'package:base':

    date, intersect, setdiff, union

Loading required package: tidyr

Attaching package: 'tidyr'

The following object is masked from 'package:magrittr':

    extract

Loading required package: dplyr

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

Attaching package: 'radiant.data'

The following objects are masked from 'package:lubridate':

    month, wday

The following object is masked from 'package:ggplot2':

    diamonds

The following object is masked from 'package:magrittr':

    set_attr

The following object is masked from 'package:base':

    date

Loading required package: radiant.design

Loading required package: radiant.basics

Loading required package: radiant.model

Loading required package: radiant.multivariate

result <- regress(
  EPL, 
  rvar = "Points", 
  evar = "Wage.Bill.milGBP"
)
summary(result)

Linear regression (OLS)
Data     : EPL 
Response variable    : Points 
Explanatory variables: Wage.Bill.milGBP 
Null hyp.: the effect of Wage.Bill.milGBP on Points is zero
Alt. hyp.: the effect of Wage.Bill.milGBP on Points is not zero

                  coefficient std.error t.value p.value    
 (Intercept)           32.116     2.749  11.683  < .001 ***
 Wage.Bill.milGBP       0.240     0.030   8.042  < .001 ***

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R-squared: 0.782,  Adjusted R-squared: 0.77 
F-statistic: 64.675 df(1,18), p.value < .001
Nr obs: 20 

library(gvlma)
gvlma(result$model)

Call:
lm(formula = form_upper, data = dataset)

Coefficients:
     (Intercept)  Wage.Bill.milGBP  
         32.1159            0.2402  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = result$model) 

                    Value p-value                Decision
Global Stat        4.8001 0.30843 Assumptions acceptable.
Skewness           0.2378 0.62583 Assumptions acceptable.
Kurtosis           0.1547 0.69412 Assumptions acceptable.
Link Function      1.5649 0.21096 Assumptions acceptable.
Heteroscedasticity 2.8428 0.09178 Assumptions acceptable.