• Create a new program to study this data. Download the dataset and save it with a short meaningful name.

• Are there any issues with the data which we need to take into account?

• plot the data in a similar style to Figure 3.1 but don’t worry about the flags or the statistics in the upper left hand corner.

• What sort of relationship does there appear to be between the two variables?

• Calculate the Pearson correlation coefficient and the Spearman rank correlation coefficient between the two variables.

• What conclusion can we draw from those coefficients?

cnd <- read.csv ("Chocolate_Nobel_data.csv")

## The Pearson correlation coefficient is: 0.7575217

## The Spearman correlation coefficient is: 0.8403233

There is a strong positive monotonic relationship between Noble Laureates per 10 million population and chocolate consumption.

• Create a plot containing four subplots (use par (mfrow = …)):

the plot from Exercise 3.1 plus versions where log() transformations have been taken of the two variables,

• individually and

• jointly.

• Which plot appears most linear? Calculate the two correlation coefficients from Exercise 3.1 for each of the four plots and insert them into the bodies of the plots

There is a powerful relationship between chocolate consumption and the number of Nobel laureates in various countries.

A correlation between X and Y does not prove causation but indicates that:

• either X influences Y,

• Y influences X,

• or X and Y are influenced by a common underlying mechanism.

Apply your favorite transformation from Exercise 3.2 to the data,

• firstly excluding Brazil and China, and

• secondly excluding all dates before 2013.

• Produce a pair of plots similar to those in Exercise 3.2.

• What conclusions can we draw from our investigations?

• Does chocolate consumption improve intellectual output (for which Noble prizes might be considered a proxy)?

• If so, why? If not, what can we conclude?

class(cnd)

## [1] "data.frame"

cnd_ex <- cnd[!(cnd$country %in% c("Brazil", "China")), ]

cnd2013 <- cnd_ex[cnd_ex$year >= 2013, ]

##        country choc_kg year Nobel_no Nobel_10m
## 1      Germany    12.2 2013      105    13.013
## 2  Switzerland    11.7 2014       25    30.125
## 3       Norway     9.6 2013       13    24.947
## 4           UK     8.9 2013      125    19.315
## 5      Austria     8.8 2013       21    24.577
## 6      Denmark     7.6 2013       14    24.695
## 7      Finland     7.2 2013        4     7.268
## 8      Belgium     6.9 2013       10     8.850
## 9       France     6.7 2013       61     9.473
## 10      Sweden     6.2 2013       30    30.677
## 11   Lithuania     5.8 2013        1     3.474
## 12       Italy     3.9 2013       20     3.345
## 13       Czech     3.6 2013        5     4.742
## 14       Spain     3.4 2013        8     1.735
## 15    Portugal     2.9 2013        2     1.932
## 16     Hungary     2.7 2013        9     9.132

There is a powerful relationship between chocolate consumption and the number of Nobel laureates in various countries.

A correlation between X and Y does not prove causation but indicates that:

• either X influences Y,

• Y influences X,

• or X and Y are influenced by a common underlying mechanism

• Expand the program that you created in Exercise 3.1 to display the two correlation coefficients to the screen.

• Send these outputs to a file which has an appropriate heading together with your name and the date and time at the bottom.

sink("output exercise 3.1 .txt")

# pearson correlation coefficient
pearson <- cor(cnd$choc_kg, cnd$Nobel_10m,
    method = "pearson")
cat ("The pearson correlation coefficient is:", pearson, "\n")

## The pearson correlation coefficient is: 0.7575217

# Spearman rank correlation coefficient
spearman <- cor(cnd$choc_kg, cnd$Nobel_10m,
    method = "spearman")
cat ("The Spearman correlation coefficient is:", spearman,"\n")

## The Spearman correlation coefficient is: 0.8403233

sink()

For the country data:

• produce a matrix of scatter plots comparing the three numerical columns of data.

You could either use:

• the pairs() function

• or explore the car package for a more sophisticated representation.

• Are any of the relationships linear? Look for best linear relationships using log() transformations and correlations.

cd_pop <- round (cd$population, digits = - 5)
cd_gdp <- round (cd$gdp_head, -2)
cd_age <- round (cd$age_median / 5) * 5
cd_cal <- round (cd$kcals_day, -2)

df_cd <- data.frame (
  population = cd_pop,
  gdp = cd_gdp,
  age = cd_age,
  kcal = cd_cal
)

df_cd_log <- data.frame (
  population = log(cd_pop),
  gdp = log(cd_gdp),
  age = log(cd_age),
  kcal = log(cd_cal)
)

I deal with non-rounded data, take them on a log-scale

• step 0: preparatory step

library(car)

## Loading required package: carData

How can I find the largest residual point?

• first, I use max function to find the value of the largest residual;

• then, I use the residual table (model_age_gdp$residual) to find which point it is (19)

• This is because the residual table have the same order as the original data.frame (df_cd_log)

• I can then say: plot me the 19th row’s (x-value is log(gdp_head), y-value is log(age_median))

• I use the original data here, instead of the rounded data in the data frame I created!

• Solid Line:

A solid horizontal line at y = 0 is often used as a reference line to indicate the expected value of residuals when the model is accurate.

In an ideal situation, residuals should be randomly distributed around this line with no discernible pattern.

• Dashed Lines:

Dashed lines are often used to indicate patterns in the residuals.

• Shaded area

In a residual plot produced by the scatterplot() function from the car package, the area typically represents a confidence band or tolerance interval for the residuals. This interval provides a visual indication of the expected range for residuals under the assumption that the model is correctly specified.