Question

Data Mining/ Data Understanding and Preparation /

Chi-Square

Q8) (7 Points) Use the following matrix to find the correlation, Chi-square correlation, between the Hot and Windy attributes. Windy Windy Sum True False Hot 10 (2) 20 (_) 30 True Hot 30 ( _) 40 (_) 70 False Sum 40 60 100

Answer 1

Here is the solution

Matthews correlation coefficient for confusion matrix data

correlation:

# Solution Given confusion matrix type data assume these as positive & negative windy (false) total I windy Trie) Hot toru) To Hot (false) 20 30 40 To Total 40 60 Correlation: Matthews correlation TP X TN-FPX EN selficient) MCC CTP+FP) (TP + FN) (TN+FP) CTN + FN) 10 X 20 - 30 X 40 MCC = (10 +30) (10+40) (20+30) (20+40) 200-120 w (40)(50) (50)(60) Mce 0.03265 TP :- Tome positive TN :- Towe Negative FP :- False positive FN : - False Negative

Chi-square correlation

From the given observed values we need to find the expected values.

For that,

# chi-square : X ² = E (Oi-E ;)² Oi - observed valuels) Ei - Expected values) For TP:- 12 TP Hotrue windy 40x30 100 true 60x30 =18 TN LOO 40x70 FP L Hot true windy false] : windy True windy False Hot False IOD s FNL Hot Goxo too false Expected valuest windy True windy false sum 2018) 30 Hot True 1012) 10 Hot false 300 28) 40(42) 60 100 Sum 40 X- 8 (0-E ) (40-42)² (10-12) (20-18) + (30-28) + + 42 28 12 18 4 4 4 4 + 12 28 92 1 4 + + + 12 42 18 x2 = 0.49365 0-443 = 4 x 25 126 = 0.79365