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Linear regression
Linear regression is one of the most popular types of predictive analysis. Linear regression involves the following two things:
Naming variables
The regression’s dependent variable has many different names. Some names include outcome variable, criterion variable, and many others. The independent variable can be called exogenous variable or repressors.
Functions of regression analysis
Breaking down regression
There are two basic states of regression-linear and multiple regression. Although there are different methods for complex data and analysis. Linear regression contains an independent variable to help forecast an outcome of a dependent variable. On the other hand, multiple regression has two or more independent variables to assist in predicting a result.
Regression is very useful to financial and investment institutions because it is used to predict the sales of a particular product or company based on the previous sales and GDP growth among many other factors. The capital pricing model is one of the most common regression models applied in the finance. The example below describes formulae used in linear and multiple regression.
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Choosing the best regression model
Selecting the right linear regression model can be very hard and confusing. Trying to model it with a sample data cannot make it easier. This section reviews some of the most popular statistical methods which one can use to choose models, challenges that you might come across, and lists some practical advice to use to select the correct regression model.
It always begins with a researcher who would like to expound the relationship between the response variable and predictors. The research team that is accorded with the responsibility to perform investigation essentially measures a lot of variables but only has a few in the model. The analysts will make efforts to reduce the variables that are different and apply the ones which have an accurate relationship. As time moves on, the analysts continue to add more models.
Statistical methods to use to find the best regression model
If you want a great model in regression, then it is important to take into consideration the type of variables which you want to test as well as other variables which can affect the response.
Modified R-squared and Predicted R-squared.
Your model should have a higher modified and predicted R-squared values. The statistics shown below help eliminate critical issues which revolve around R-squared.
• The adjusted R squared increases once a new term improves the model.
• Predicted R-squared belongs to the cross-validation that helps define the manner in which your model can generalize remaining data sets.
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P-values for the Predictors
When it comes to regression, a low value of P denotes statistically significant terms. The term “Reducing the model” refers to the process of factoring in all candidate predictors contained in a model.
Stepwise regression
This is an automated technique which can select important predictors found in the exploratory stages of creating a model.
Real World Challenges
There are different statistical approaches for choosing the best model. However, complications still exist.
• The best model happens when the variables are measured by the study.
• The sample data could be unusual because of the type of data collection method. A false positive and false negative process happens when you handle samples.
• If you deal with enough models, you’ll get variables that are significant but only correlated by chance.
• P-values can be different depending on the specific terms found in the model.
• Studies have discovered that the best subset regression and stepwise regression can’t select the correct model.
Finding the correct Regression Model
Theory
Perform research done by other experts and reference it into your model. It is important that before you start regression analysis, you should develop ideas about the most significant variables. Developing something based on outcome from other people eases the process of collecting data.
Complexity
You may think that complex problems need a complex model. Well, that is not the case because studies show that even a simple model can provide an accurate prediction. Once there is a model with the same explanatory potential, the simplest model is likely to be the perfect choice. You just need to start with a simple model as you slowly advance the complexity of the model.
How to calculate the accuracy of the predictive model
There are different ways in which you can compute the accuracy of your model. Some of these methods include:
2. Another method is to calculate the “Confusion Matrix” to the computer False Positive Rate and False Negative Rate. These measures will allow a person to choose whether to accept the model or not. If you consider the cost of the errors, it becomes a critical stage of your decision whether to reject or accept the model.
