1. 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.

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

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