Data on the amount of the customers' shopping by using an account card and whether they decided to upgrade their account from silver status to platinum status after receiving the upgrade offer is shown in Table 2.

1. Construct the k nearest neighbors scheme for predicting upgrades based on the data given in Table 2, and interpret the confusion matrix.

2. According to the data given in part 1, estimate the probability of upgrade for each division of the purchase amount, using Bayes' theorem.

Table 2

Data on the Amount of Shopping and the decision to Upgrade

UpGrade Purchases PlatProfile RowNear 1 RowNear 2 RowNear 3 RowNear 4 O 7.471 7 40 26 29 C 33 25 2N 21.142 10 14 39.925 17 19 37 38 32.450 32 22 39 38 48.950 9 11 31 24 28.520 35 20 32 4 7.822 1 26 29 O 26.548 36 13 25 33 48.831 11 31 24 17.584 14 2 29 33 49.820 9 31 15 50.450 N 18 28 23 13 28.175 8 34 25 14 16.200 29 2 33 15 52.978 W 27 11 5 16 58.945 27 15 31 1 1 17 40.075 37 19 38 18 42.380 28 23 12 21 19 38.110 W 17 38 39 20 26.185 35 6 32 4 0 52.810 18 28 23 N 22 34.521 38 4 19 23 34.750 28 34 13 24 46.254 5 11 37 25 24.811 33 8 36 13 26 4.792 7 40 29 55.920 16 31 11 28 38.620 23 30 34 29 12.742 40 10 7 30 31.950 34 23 13 36 51.211 15 5 9 32 30.920 6 35 22 33 23.527 25 2 8 36 34 30.225 30 13 36 8 35 28.387 20 32 4 36 27.480 O 13 8 25 34 37 41.950 3 19 24 38 34.995 39 22 4 19 39 34.964 22 4 19 40 O 7.998 1 26 29 41 42.571 O -0 42 51.835