Consider the following hypothetical dataset providing measurements for Average Steps per day and Average Resting Heart Rate, across a sample of 12 people.
Person ID Average Steps per day Average Resting Heart Rate
1 1000 100
2 2500 105
3 3000 80
4 5000 77
5 6000 74
6 9000 70
7 11000 65
8 14000 63
9 18000 62
10 19000 61
11 19500 60.5
12 22000 55
Visually, the data looks like this:
1. Compute the Pearson correlation between Average Steps per day and Average Resting Heart Rate. Show your working. How would you interpret this correlation value?
2. Based on the Pearson correlation value, can one conclude that doing more steps per day will cause one’s average resting heart rate to decrease? How else might it be interpreted?
3. Discretise the data as follows: Apply 3 bin equal frequency discretisation to Average Steps per day and 4 bin equal frequency discretisation to Average Resting Heart Rate. Show the values of the discretised features.
4. Using the discretised features, compute the entropies: H(Average Steps per day), H(Average Resting Heart Rate), H(Average steps per day | Average Resting Heart Rate), H(Average Resting Heart Rate | Average Steps per day).
5. Using the above information, compute the mutual information between Average Steps per day and Average Resting Heart Rate.
