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**Hello everybody, today let’s exercise our knowledge !**

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**Q1. **

Calculate the following lift values for the table correlating Burger & Chips below:

LIFT (Burger, Chips)

LIFT (Burger, ^Chips)

LIFT (^Burger, Chips)

LIFT (^Burger, ^Chips)

Please also indicate if each of your answers would suggest independent, positive correlation, or negative correlation.

Column1 |
Chips |
^Chips |
Total Row |

Burgers | 600 | 400 | 1000 |

^Burgers | 200 | 200 | 400 |

Total Column | 800 | 600 | 1400 |

**Answer **

LIFT (Burgers, Chips)

s (Burgers u Chips) = 600/1400 = 0.428

s(Burgers) = 1000/1400 = 0.714

s(Chips) = 800/1400 = 0.571

LIFT (Burgers, Chips) = 0.428/(0.714*0.571) = 1.049

LIFT (Burgers, Chips) > 1

*My answer suggests that Burgers and Chips are positively correlated.*

LIFT (Burgers, ^Chips)

s(Burgers u ^Chips) = 400/1400 = 0.285

s(Burgers) = 1000/1400 = 0.714

s(^Chips) = 600/1400 = 0.428

LIFT (Burgers, ^Chips) = 0.285/(0.714*0.428) = 0.932

LIFT (Burgers, ^Chips) < 1

*My answer suggests that Burgers and ^Chips are negatively correlated.*

* *

LIFT (^Burgers, Chips)

s(^Burgers u Chips) = 200/1400 = 0.142

s(^Burgers) = 400/1400 = 0.285

s(Chips) = 800/1400 = 0.571

LIFT (^Burgers, Chips) = 0.142/(0.285*0.571) = 0.872

LIFT (^Burgers, Chips) < 1

*My answer suggests that ^Burgers and Chips are negatively correlated.*

LIFT (^Burgers, ^Chips)

s(^Burgers u ^Chips) = 200/1400 = 0.142

s(^Burgers) = 400/1400 = 0.285

s(^Chips) = 600/1400 = 0.428

LIFT (^Burgers, ^Chips) = 0.142/(0.285*0.428) = 1.164

LIFT (^Burgers, ^Chips) > 1

**–***Burgers and Chips are positively correlated.*

**Q2.**

calculate the following lift values for the table correlating Ketchup & Shampoo below:

- LIFT (Ketchup, Shampoo)
- LIFT (Ketchup, ^Shampoo)
- LIFT (^Ketchup, Shampoo)
- LIFT (^Ketchup, ^Shampoo)

indicate if each of your answers would suggest independent, positive correlation, or negative correlation.

Column1 |
Shampoo |
^Shampoo |
Total Row |

Ketchup | 100 | 200 | 300 |

^Ketchup | 200 | 400 | 600 |

Total Column | 300 | 600 | 900 |

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**Answer Q2.**

LIFT (Ketchup, Shampoo)

s(Ketchup u Shampoo) = 100/900 = 0.111

s(Ketchup) = 300/900 = 0.333

s(Shampoo) = 300/900 = 0.333

LIFT (Ketchup, Shampoo) = 0.111/(0.333*0.333) = 1.001

LIFT (Ketchup, Shampoo) = 1

*My answer suggests that Ketchup and Shampoo are independent.*

* *

LIFT (Ketchup, ^Shampoo)

s(Ketchup u ^Shampoo) = 200/900 = 0.222

s(Ketchup) = 300/900 = 0.333

s(^Shampoo) = 600/900 = 0.666

LIFT (Ketchup, ^Shampoo) = 0.222/(0.333*0.666) = 1.001

LIFT (Ketchup, ^Shampoo) = 1

*My answer suggests that Ketchup and Shampoo are independent.*

LIFT (^Ketchup, Shampoo)

s(^Ketchup u Shampoo) = 200/900 = 0.22

s(^Ketchup) = 600/900 = 0.67

s(Shampoo) = 300/900 = 0.33

LIFT (^Ketchup, Shampoo) = 0.222/(0.666*0.333) = 0.22/0.22 = 1.001

LIFT (Ketchup, Shampoo) = 1

*My answer suggests that Ketchup and Shampoo are independent.*

LIFT (^Ketchup, ^Shampoo)

s(^Ketchup u ^Shampoo) = 400/900 = 0.444

s(^Ketchup) = 600/900 = 0.666

s(^Shampoo) = 600/900 = 0.666

LIFT (^Ketchup, ^Shampoo) = 0.444/(0.666*0.666) = 1.001

LIFT (Ketchup, Shampoo) = 1 (Ketchup and Shampoo, Independent)

*Ketchup and Shampoo are independent. *

**Q3. **

calculate the following chi Squared values for the table correlating Burger and Chips below (Expected values in brackets).

- Burgers & Chips
- Burgers & Not Chips
- Not Burgers & Chips
- Not Burgers & Not Chips

For the above options, also indicate if each of your answer would suggest independent, positive or negative correlation.

Column1 |
Chips |
^Chips |
Total Row |

Burgers | 900 (800) | 100 (200) | 1000 |

^Burgers | 300 (400) | 200 (100) | 500 |

Total Column | 1200 | 300 | 1500 |

**Q4: **

calculate the following chi squared values for the table correlating burger and sausages below (Expected values in brackets).

- Burgers & Sausages
- Burgers & Not Sausages
- Sausages & Not Burgers
- Not Burgers and Not Sausages

For the above options, please also indicate if each of your answer would suggest independent, positive correlation, or negative correlation?

Column1 |
Chips |
^Chips |
Total Row |

Burgers | 800 (800) | 200 (200) | 1000 |

^Burgers | 400 (400) | 100 (100) | 500 |

Total Column | 1200 | 300 | 1500 |

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**Answer Q4**

Χ^{2 }= (800-800)^{2 }/ 800 + (200-200)^{2 }/ 200 + (400-400)^{2 }/ 400 + (100-100)^{2 }/ 100

= 0^{2 }/ 800 + 0^{2 }/ 200 + 0^{2 }/ 400 + 0^{2 }/ 100 = 0

Burgers & Chips, Independent Χ^{2 }= 0.

**Burgers & Chips– Observed & Expected, 800 – Independent**

**Burgers & ^Chips – Observed & Expected, 200 – Independent**

**^Burgers & Chips – Observed & Expected, 400 – Independent**

**^Burgers & ^Chips – Observed & Expected, 100 – Independent**

**Q5:**

Under what conditions would Lift and Chi Squared analysis prove to be a poor algorithm to evaluate correlation/dependency between two events?

*The conditions under Lift & Chi Squared analysis that could prove to be a poor algorithm to evaluate correlation / dependency between two events are when there are too many null transactions observed.*

Suggest another algorithm that could be used to rectify the flaw in Lift and Chi Squared?

*Another algorithm that could be used to rectify the flow in Lift & Chi squared is: AllConf, Cosine, Jaccard, MaxConf, Kulczynski.*