Correlation

1. What does the correlation analysis study do? Explain with a numerical example.  Deadline Tuesday 8pm.

Answer:

1. Correlation Analysis Study gives us a medium for detecting and measuring the relationship between two variables. For instance: The table below shows the quantity of petrol consumed by each Salesman of a reputable pharmaceutical company along with the number of cartons (quantity) sold.

2. An independent variable is one that can be manipulated. In the equation y=f(x), y is considered as the dependent variable and x as the independent variable. For example; Resumption time at Work will be an independent variable where Volume of Traffic will be the dependent variable. In the example below Quantity Sold is the independent variable while Petrol consumed is the dependent variable.

NDX | Salesman | Petrol Consumed (Litres) | Quantity Sold |

01 | A. J. Johnson | 50 | 200 |

02 | Peter Brown | 60 | 215 |

03 | T. Williams | 20 | 100 |

04 | S. Paulson | 60 | 250 |

05 | K. Okocha | 100 | 50 |

06 | T. Badoo | 25 | 120 |

07 | S. A. Brown | 7 | 30 |

08 | Saka Jojo | 60 | 300 |

09 | F. Dunka | 40 | 280 |

10 | K. Court | 50 | 280 |

A direct observation of the data above shows a relationship between the petrol consumed by these salesmen and the quantity of products sold i.e. the more petrol used the higher the number of products sold. This may be generalistic though but it will be observed that some aberrations may be present for instance while K. Okocha consumed more petrol than T. Badoo but sold fewer products as reflected in the Scatter Diagram below.

3. Correlation analysis study involves the measure of the relationship between for example the amount of petrol consumed and the number of products sold. One technique is to use the correlation co-efficient.

H0 = The Correlation between the quantity of petrol consumed and quantity of products sold is positive

H1 = There is no relationship between the two variables

Petrol Consumed (X) has a...