Ch2. Expert example: ill-conditioned simple regression problem about lmlcr HOT 2 CLOSED

This is the exercise I started writing...

Let's consider the Wine Quality dataset (winequality-all.csv)
that you can download from SIT114's CloudDeakin site
(Resources → Datasets). It is assumed that the file is stored in
the same current working directory (e.g., the same where the Rmd file is).

wines <- read.csv("winequality-all.csv", comment="#")
head(wines)

These are Vinho Verde red and white wine samples from the north of Portugal,
see https://www.vinhoverde.pt/en/homepage.
There are 11 physicochemical features reported.
Moreover, there is a wine rating on the scale 0 (bad) to 10 (excellent)
given by wine experts, read more at
https://archive.ics.uci.edu/ml/datasets/Wine+Quality.

1. Remove all the red wines from wines (replacing the old data frame
   with the new one). Then, get rid of the color and response columns.

   Click here for a solution

   First let's handle the red wines.

   wines <- wines[wines$color != "red", ]
   

   Omitting the aforementioned columns can be done in a few ways. Here is one:

   wines <- wines[, is.na(match(names(wines), c("color", "response")))]
   

   To recall, names(data.frame) gives the vector of column names.
   On the other hand, the match() function, matches all the values
   in the first argument against all the values in the second argument.
   If there is no match (in our case, if a column name is not amongst
   the two names we wish to remove), NA is generated.

2. Compute the Pearson correlation coefficient between alcohol and
   every other variable in the dataset.

   Click here for a solution

   This can be done via a call to cor(). A quick glimpse at the manual page
   (?cor) reveals, that this task can be solved as follows:

   cor(wines$alcohol, wines)
   

   We could have got rid of the the alcohol vs. alcohol comparison,
   but wanted to show that any column is always perfectly linearly correlated
   with itself, hence the 1.0 coefficient obtained.

3. Fit simple regression models for alcohol as functions
   of the three most correlated variables (three individual models).

round(cor(wines),2)

f_density <- lm(alcohol~density, data=wines)
plot(alcohol~density, data=wines)
summary(f_density)
abline(f_density, col="red")

step(lm(alcohol~1, data=wines), # empty model
    scope=formula(lm(alcohol~., data=wines)), # full model
    direction="forward")

from lmlcr.

(the to-do list has moved)

from lmlcr.