Linear Regression, also know as "trend line analysis", is a statistical technique for predicting the outcome of a future event based on knowledge of similar events of the past.
For example: Increasing the advertising budget has always provided an increase in sales. You want to know how much should the advertising budget be increased to produce sales of x amount. Or, if you add x dollars to the advertsing budget what would the resulting sales be. Or, compare vaious trend lines for media effectiveness and insertion planning.
The slope (trend line) is an imaginary straight line that best represents the trend in the events of the past. You could simply plot the past datapoints and "guesstimate" the line that best represents it but this is a hit or miss situation.
In addition to providing a slope factor, this program also provides a value known as the "coefficient of determination". This value, ranging from 0 to 1, describes how well the line correlates to the data. A value close to 1 is a high correlation. A value close to 0 is a low correlation, meaning predictions based on the line will be relatively inaccurate.
As a demonstration let's say your sales manager is spending big bucks on an applicant screening test for potential sales persons. Do the test result actually mean anything? Does a higher score mean higher performance overall? How well do the test scores correlate to actual performance?
Test Score Performance
(x) (y)
5 10
13 30
8 30
10 40
15 60
20 50
4 20
16 60
18 50
6 50
Run the program and enter the data above as prompted. If you make a mistake, at the x datapoint prompt you can back an entry out by entering is as a negative value, also enter the same y datapoint value when prompted.
When all of the datapoints have been entered, enter "0" to stop the data entry and compute the slope, y intercept, and correlation factor of the data. If the correlation factor is near zero the data is practically worthless - continue gathering data. If its high (near 1), then predictions can be reasonably made and/or ploted.
After the slope, y intercept, and correlation values have been displayed a Menu type selection is displayed.
To find what a given test score could produce enter a "1" - Find X. This finds an entered x (test score) value on the slope and returns the corresponding y (performance) value.
To find what typical test score would indicate a given level of performance enter a "2" - Find Y. This finds an entered y (performance) value on the slope and returns the corresponding x (test score) value.
To EXIT the program enter a "0". The only acceptable entries are "0", "1", and "2", any other entry simply loops back to the prompt dialog.
