In order to make predictions, we first must examine the distribution of the data given. From this data, we can make a prediction about the problem being assessed.

A predictor variable can be defined as a variable which is used to estimate some characteristic or response. A regression analysis which involves only one predictor is called Simple Linear Regression Analysis. Even though a single predictor may oversimplify the estimation in real systems, the results that are obtained can be easily extended to real systems.

Let's look at the two examples.

Example 1:

A cost modeller wants to know the cost for a new contract based on the data collected from the previous contracts.

We must examine the data collected from previous contracts, in order to make any prediction as to how much a new contract would cost.

Estimated cost of previous contracts

Number of employees x	Total cost of contract(in $1000's) y
10	13
9	11
8	12
7	10
6	8
5	6
4	5
3	3
2	4
1	3

We see from the table that the values of x are fixed and when the values of y are subject to random variation, the problem is to find a line of best fit that relates y to x. This line is called the regression line of y on x and the equation of the line is called a regression equation. Thus, the values of y will not occur exactly on the regression line.

Example 2:

Suppose we wanted to predict a student's grade on a freshman college calculus midterm based on his/her SAT score.

We must examine the SAT scores and calculus midterm scores achieved by former students, in order to make any prediction as to how well a student would do on the calculus midterm.

SAT Scores and Calculus Midterm Scores of 10 former students

Student	SAT Score x	Calculus Midterm Score y
1	1100	89
2	1300	92
3	1000	86
4	1100	92
5	1200	90
6	1200	93
7	1400	98
8	1300	95
9	1000	88
10	1400	95

We have examined the data collected from past experiences and this data is called the population. We will use this data in our predictions and we will see how the analysis is carried out in the next page.