The Borrower

Part II

Descriptive Statistics

Chapter 4: Descriptive Methods in Regression and correlation

Introduction

We are interested to know whether two or more variables are related, and how are they related.

4.1 Linear equation with one independent variable

Definition: y-intercept and slope

For a linear equation, the number is called the y-intercept and the number is called the slope.

(0,)

I unit increase

units up

(0,)

I unit increase

units up

Variables: x, y Independent variable-x Dependent variable-y Constants:

Examples:

Y-intercept= slope=

Y-intercept= slope=

2 Y-intercept= slope=

Note: The graph of a linear equation with one independent variable is a straight line.

Graphical interpretation of slope

>0

<0

=0

>0

<0

=0

Y increases as x increases | Y decreases as x increases | No change in y as x changes |

4.2 The regression equation (This is different from exact relationship)

* Example: (exact relationship)

An invitation card printing company charges a fixed amount $20 for each order and charging $0.5 for each invitation cards. Suppose denotes the total cost for an order and denotes the number of invitation cards to be printed for that order, write down an equation.

Suppose if you need to print 50 invitation cards what is the total cost?

Example: (Statistical relationship)

Suppose we would like to know the price of the car based on its age. It is noticed that for a fixed age of car the price varies from car to car. Suppose there is a data on age and price for a sample of cars for a particular model. How do we response if someone needs to know the price of a car based on the age?

Suppose the following data set provides average age of a car and price and if you want to buy a 5 year old car, how much you would spend on that purchase?

Age (years) | Price (‘100) |

5 | 85 |

4 | 103 |

6 | 70 |

5 | 82 |

5 | 89 |

6 | 66 |

2 | 169 |

7 | 70 |

*...