Regression is a statistical method for trying to make sense of a lot of data. The simplest form of regression is linear regression. It's goal is to show that your data has a high correlation to a straight line. Correlation has a range of 0 to 1. When you have performed your linear regression on your data, a correlation close to 1 gives you confidence to believe that your data is closely related to a straight line.
When using regression analysis, which of the following is of importance:
1. the size of the regression slope coefficient 2. the sign of the regression slope coefficient 3. the significance of the regression slope coefficient 4. the sign, size, and significance of the regression slope 5. the sign, size, and significance of the correlation coefficient
To begin with I am going to assume that you are talking about simple linear regression. Regression can be applied to many different kinds of curves, such as logarithmic, exponential and multivariate, but this answer would become much too complex and long if they were addressed.
The real value of regression analysis is prediction. If your regression is time based then you can predict the future, assuming that the things that effect the data do not change. So the questions that you want to ask are the following.
1. How close does your data fit the model (regression line) that you have created. 2. What are the parameters of the regression line? If you know the parameters of the line you can predict past the data that you have.
The answer to the first question is found in the correlation coefficient. It has a range of -1 to +1. You want it to be as close to +1 as possible. If it gets below +.5, then it probably is not a very good predictor. It is easily calculated from the data analysis
The answer to the second question is the derived equation for the straight line from your regression analysis. The simple equation is of the form y=ax+b. The y and x are variables, but a and b are constants. A is the slope of the curve and b is simply the vertical offset from the origin when x=0. With a and b known, you can recreate the regression line on any graph paper or electronic graph. These constants are also easily calculated from the data.
So there are 2 things to know when regression modeling. The first is the correlation. It will tell you how good your model really is. The second is the derived equation of the regression line. It will let you make predictions beyond the data that you have available.