Bit More About Regression

An extension of the correlation, a regression allows you to compare your data looks to a specific model: a straight line. Instead of using a normal curve (bell-shaped hump) as a standard, regression draws a straight line through the data. The more linear your data, the better it will fit the regression model.Once a line of regression is drawn, it can be used to make specific predictions. You can predict how many shoes people will buy based on how many hats they buy, assuming there is a strong correlation between the two variables.

Just as a correlation can be seen in a scatterplot, a regression can be represented graphically too. A regression would look like a single straight line drawn through as many points on the scatterplot
as possible. If your data points all fit on a straight line (extremely unlikely), the relationship between the two variables would be very linear.

Most likely, there will be a cluster or cloud of data points. If the scatterplot is all cloud and no trend, a regression line won’t help…you wouldn’t know where to draw it: all lines would be equally bad.

But if there the scatterplot reveals a general trend, some lines will obviously be better than others. In essence, you try draw a line that follows the trend but divides or balances the data points equally.

In a positive linear trend, the regression line will start in the bottom left part of the scatterplot and go toward the top right part of the figure. It won’t hit all of the data points but it will hit most or come close to them.

You can use either variable as a predictor. The choice is yours. But the results mostly likely won’t be the same, unless the correlation between the two variables is perfect (either +1 or -1). So it matters which variable is selected as a predictor and which is characterized as the criterion (outcome variable).

Predicting also assumes that the relationship between the two variables is strong. A weak correlation will produce a poor line of prediction. Only strong (positive or negative) correlations will produce accurate predictions.