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...

Using spreadsheet packages

Standard spreadsheet packages such as Excel can perform multiple regression analysis and are sufficient for most routine tasks. A regression equation can be calculated via menus and dialogue boxes and no knowledge of the formulae is required. However, when problems such as autocorrelation (see below) are present, specialised packages such as TSP, Microfit or Stata are much easier to use and provide more comprehensive results. We also introduce a new example in this section, estimating a demand...

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(iv) If someone aged 50-59 is drawn at random from the economically active population, the probability of their being unemployed for eight weeks or less is 8.9 . (v) The probability of someone aged 35-49 drawn at random from the economically active population being unemployed for between 8 and 26 weeks is 0.166 x 521.2 4900. (c) A person is drawn at random from the population and found to have been unemployed for over one year. What is the probability that they are aged between 16 and 19 'Odds'...