Title: Understanding coefficients
Course: UGQuants (SSPS) > Section: Correlation and Regression

Understanding coefficients

In the final part of the SPSS output labelled 'coefficients', SPSS calculates the value of ‘a’ (the intercept) and ‘b’ (the slope) in our regression equation.  These may be located under the column heading 'Unstandardised Coefficients'. The intercept, or 'a' is referred to by SPSS as the constant. The value of 'b' appears just underneath the value of the constant, against the name of the independent (or X-axis) variable.  The simplest way to interpret the coefficient is that a one unit increase in the independent variable produces a ‘b’ change in the dependent variable. Using our example, a one unit increase in hours worked per week in a person's main job produces a .129 decrease in hours spent on housework.

We are also interested in whether the coefficient is significantly different from zero.  To evaluate this we can look at two pieces of information.  First, we can look at the relationship between the unstandardized coefficient and the standard error. A signficiant coefficient tells us whther the slope (b) is statistically different zero (in other words, from a horizontal line). To tell if the slope equals zero we perform a z test.  The unstandardized coefficient must be greater than 1.96 times the standard error for it to be significant at the 5% level, and 2.58 times greater for it to be significant at the 1% level. These numbers, 1.96 and 2.58, are the critical values in the normal curve. 95% of the values in a normal curve will lie between 1.96 below and 1.96 above the mean.  In other words, if the coefficient is more than twice as large as the standard error then we have reason to believe that the coefficient is significantly different from zero.

The other piece of information we might look at is the ‘p’ value, listed here under the ‘sig’ column. This provides us with a measure of significance directly. If the p value is less than .05 then we say that the coefficient is significant at the .05 level. In other words, there is a 5 % chance that we are saying the coefficient is significantly different from zero when in fact it is not.  If the p value is less than .01 then there is a 1% chance of making this type of error.  The significance levels that are typically used vary across the disciplines in the social sciences – some highlight coefficients significant at the .1 or .001 level - but .05 and .01 are the most common.

Standardized and unstandardized coefficients

There are in fact two types of regression coefficients: unstandardized and standardized.  Most statistical software packages will produce both types of coefficients.  The unstandardized coefficients are in their original units of measurement.  If, for example, we wanted to know what impact age had on income, and the coefficient was 103, we would say that a one unit increase in age (which in this case might be a one year increase in age) would lead to a £103 increase in income.

Sometimes, however, we don’t care very much what the original units of measurement are and we want to look at the standardized coefficients. To create standardized coefficients we divide the original coefficient for a variable by the standard deviation of that variable.  This is more useful for multiple regression when we might want to compare the performance of coefficients across different variables.