The charts even show the parameter values for a standard (OLS) linear regression model for comparison (as indicated by the red line). Figure 3 – Separate regression parameter estimates for different quantiles The new Quantile regression procedure even plots these values as shown in figure 3. As such, Quantile regression produces separate coefficients and intercept values for each requested quantile. However, there’s no reason to assume that the same formula applies to the data in the top 10% of the current salary distribution, or the say, the bottom 25%. The formula also contains a constant value (or intercept) of $1,928. This formula consists of a single coefficient of 1.9, meaning that for every extra dollar of beginning salary, the respondent earns $1.9 dollars in their current salary. Using standard Linear Regression on the same dataset we get a single formula for estimating a respondent’s current salary. The effect of this is that we can produce separate predictions for the different parts of the dependent variable’s distribution. Figure 2 – Quantile regression showing different lines of fit for separate percentiles For example, we can request estimates for the lowest 10 percent (quantile = 0.1) or the top 90 percent (quantile = 0.9) of the dependent variable. In other words, we can fit separate regression lines for different percentiles. Although there’s no reason to believe that a regression based on line fitted about the median would be more accurate than one based on a mean, quantile regression is flexible enough to allow us to fit a model based on other percentile values. We should bear in mind that a median is also called the 50 th percentile and in this context percentile and quantile refer to the same thing. Quantile regression offers us the opportunity to fit the model using a median value rather than a mean. Technically, this is referred to as ‘heteroscedasticity’, but more prosaically, it just indicates that the model is likely to be worse at estimating higher values than lower ones since the points vary more about the line. You may note from the chart that there seems to be a slight ‘funnelling’ of the points near the higher values in the scatterplot. This line can be used to estimate the mean value of the dependent variable as represented by the points clustering about line at a given value of the independent (predictor) variable (see figure 1) Figure one: regression using mean least squares function In standard ‘least squares’ regression the model predictions are based on a single regression line. New analytical procedures Quantile Regression If you’re an existing SPSS user and you’d like to upgrade to v26 there’s more information about how to do that here. If you’re interested in trying SPSS Statistics for the first time then do please get in touch – we’ll be happy to help. Version 26 introduces a number of additional analysis procedures as well as new command enhancements. And, with self-service and built-in expertise and intelligence, you have the freedom and confidence to make smarter decisions that better address your business imperatives.In April of this year, IBM released the latest version of SPSS Statistics. You can uncover insights more quickly and easily from all types of data-even big data-and on multiple platforms and devices. IBM ®'s next-generation business analytic solutions help organizations of all sizes make sense of information in the context of their business. This straightforward, pragmatic reference manual will help: professional marketers who use statistical procedures in in IBM ® SPSS Statistics undergraduate and postgraduate students where marketing research and research methodology are taught all researchers analyzing survey-based data in a wide range of frontier domains like psychology, finance, accountancy, negotiation, communication, sociology, criminology, management, information systems, etc. It is widely employed in companies and many business schools also use this software package. The program uses a simple drag-and-drop menu interface, which is also suitable for non-experienced programmers. IBM ® is one of the largest statistical software providers world-wide and their IBM ® SPSS Statistics software offers a very user-friendly environment. In an accessible and step by step approach, the authors show readers which procedures to use in which particular situation and how to practically execute them using IBM ® SPSS Statistics. Marketing researchers, companies and business schools need to be able to use statistical procedures correctly and accurately interpret the outputs, yet generally these people are scared off by the statistics behind the different analyses procedures, thus they often rely on external sources to come up with profound answers to the proposed research questions.
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