However, going into greater detail concerning these issues would be beyond the scope of this paper. However, depending on the depth and range of the extant literature, the initial focus of the case study may be quite focused or broad and open-ended. Therefore and because the case study strategy is ideally suited to exploration of issues in depth and following leads into new areas of new constructions of theory, the theoretical framework at the beginning may not be the same one that survives to the end HARTLEY,p.
The Danger of Extrapolation in Regression Analysis Posted on by ahmadjohari Regression analysis is a valuable tool in statistical analysis primarily because it allows analysts to predict, or regress as we prefer to call it, variables from sets of other variables.
This method is one of the technique utilized in predictive analytics. Predictive analytics is a powerful arsenal to have in most scenarios as it allows users to envision what an outcome might be based on several inputs derived as a mathematical model.
Therein lies a problem. In my experience, I have encountered extrapolation being used to predict values for which the mathematical models do not support. Frequently, my audiences can be confused by my initial reaction towards not using extrapolation. This experience is an anecdote by the way.
I do not have any statistical proof of it. However, I am certain that many of you in the statistical field would identify with this scenario. An Example using Natural Data Set Let us consider a simple example, as shown in the chart below, showcasing the correlation between height and weight of a certain sample taken to represent a certain population.
For the purpose of this example, let us assume that all the proper statistical techniques of population sampling and hypothesis tests have been correctly undertaken. In a real example, we of course do not want to make all these assumptions; we would actually conduct all the necessary statistical procedures.
However, showing that would divert us from our topic of extrapolation. In statistics, we know that this mathematical model only holds true for weight values between 45 kg the minimum and 94 kg the maximum from the data set. This can be seen in the equation.
In the real world, if weight is 0 kg, it necessitates us to conclude that there are no subjects being measured, and therefore height can be input as 0 cm. This is of course illogical. Similarly, on the other end of the spectrum, if we were to predict height using a weight value of say, kg, you would get the value of This would be hardly true in the real world as well.
This is not an error of the mathematical model. It is simply due to the fact that our sample data has only been collected for weights between the two ranges mentioned above. Due to that, the mathematical model only holds true for those ranges.
To predict values beyond them, we would need to gather samples that span other weight ranges, perhaps by increasing the sample size. The example above shows the danger of extrapolation using a natural data set, that of height and weight.
It does not seem dangerous enough. However, in other settings, like businesses, it can have crippling effects. A Practical Example Consider the chart below, which shows a correlation between volumes sold of a particular product which have slight price differences in different regions, along with the sales revenue that they bring.
Again, let us assume that all the proper statistical procedures have been done. The chart seems to show a near perfect correlation. These are the kinds of charts that may make audiences filled with excitement.Depending on how sophisticated you want to be in interpreting data, you may run regression analysis to estimate, for example, the relationships between the various determinants of .
Multiple Linear Regression Analysis. Multiple linear regression analysis is an extension of simple linear regression analysis, used to assess the association between two or more independent variables and a single continuous dependent variable.
Depending on the analysis used, at least 15 years data may be required for reliable results. Variables and sources A large number of variables could be listed that would give information on the various habitats or ecosystems. Regression analysis is a quantitative tool that is easy to use and can provide valuable information on financial analysis and forecasting.
Find out how.
Trading. This chapter is only going to provide you with an introduction to what is called “Multiple • You use correlation analysis to find out if there is a statistically significant • You use linear regression analysis to make predictions based on the relationship that exists between two variables.
Scenario analysis has been used by the private In the develop-ing world, scenarios have been used to high-light the opportunities, risks, and trade-offs in tional or corporate strategy. Scenario Analysis for Capital Investments Scenario analysis is extensively used in the.