## The line of best fit

Is close (but not identical) to the actual birth rate of 30. The difference reflects the absence of perfect correlation between the two variables. The difference between the actual value, Y, and the predicted value, z, is called the error or residual. It is labelled e in Figure 7.4. Why should such errors occur The relationship is never going to be an exact one for a variety of reasons. There are bound to be other factors besides growth which affect the birth rate (e.g. the education of women)...

## Rule of thumb for hypothesis tests

A quick and reasonably accurate method for establishing whether a coefficient is significantly different from zero is to see if it is at least twice its standard error. If so, it is significant. This works because the critical value (at 95 ) of the t distribution for reasonable sample sizes is about 2. Sometimes regression results are presented with the t statistic (as calculated above), rather than the standard error, below each coefficient. This implicitly assumes that the hypothesis of...

## Are the results significant

These results come from a (small) sample, one of many that could have been collected. Once again we can ask the question, what can we infer about the population (of all developing countries) from the sample Assuming the sample was drawn at random (which may not be justified) we can use the principles of hypothesis testing introduced in Chapter 5. As usual, there are two possibilities 1 The truth is that there is no correlation (in the population) and that our sample exhibits such a large...

## What determines the birth rate in developing countries

This example follows the analysis in Michael Todaro's book, Economic Development in the Third World (3rd edn, pp. 197-200) where he tries to establish which of three variables (GNP per capita, the growth rate per capita, or income inequality) is most important in determining a country's birth rate. (This analysis has been dropped from later editions of Todaro's book.) The analysis is instructive as an example of correlation and regression techniques in a number of ways. First, the question is...