Here at Alchemer, we offer hands-on application training events during which customers learn how to become super users of our software.
The data collected from these feedback surveys allows us to measure the levels of satisfaction that our attendees associate with our events, and what variables influence those levels of satisfaction.
Could it be the topics covered in the individual sessions of the event? The length of the sessions? The food or catering services provided? The cost to attend? By performing a regression analysis on this survey data, we can determine whether or not these variables have impacted overall attendee satisfaction, and if so, to what extent. This information then informs us about which elements of the sessions are being well received, and where we need to focus attention so that attendees are more satisfied in the future.
Regression analysis is a reliable method of identifying which variables have impact on a topic of interest. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other. The topics covered, length of sessions, food provided, and the cost of a ticket are our independent variables.
Administering surveys to your audiences of interest is a terrific way to establish this dataset. Your survey should include questions addressing all of the independent variables that you are interested in. To begin investigating whether or not there is a relationship between these two variables, we would begin by plotting these data points on a chart, which would look like the following theoretical example. Plotting your data is the first step in figuring out if there is a relationship between your independent and dependent variables.
Our dependent variable in this case, the level of event satisfaction should be plotted on the y-axis, while our independent variable the price of the event ticket should be plotted on the x-axis. X and Y are variables and will take on different values at different points in time. The values of a and b are substituted in the regression equation to get the relationship between X and Y as follows:.
This can also be expressed in the context of the example or question making the relationship more meaningful. The intercept of This is because when advertising spend is zero, it zero is multiplied by the slope or b here This is added to your intercept, leaving you only the intercept value The coefficient b here It is also referred to as the slope of the line in a simple linear equation.
If the coefficient of the independent variable X is positive, it indicates for every unit increase in the independent variable; the dependent variable will increase by the value of the coefficient. This also means that for every unit decrease in the independent variable, the dependent variable will decrease by the value of the coefficient.
On the other hand, if the coefficient of the independent variable X is negative, for every unit increase in the independent variable, the dependent variable will decrease by the value of the coefficient. Correspondingly, for every unit decrease in the independent variable, the dependent variable will increase by the value of the coefficient. We have only one independent variable in this example.
Since you have only one independent variable, it is called simple linear regression. When you have more than one independent variable, it will be called multiple regression. Therefore, you will see a coefficient for every independent variable in the multiple regression output. The interpretation of these coefficients will be the same.
In the previous chapter, we understood the regression equation and how good or reliable the regression is. We also learned how to find the intercept and coefficients of the regression equation.
The standard error of the coefficients reflects the variability of the coefficient. In other words, when we use the regression model to estimate the coefficient of an independent variable, the standard error shows you how wrong the estimated coefficient could be if you use it to make predictions. Again, because the standard error reflects how wrong you could be, we want the standard error to be small in relation to its coefficient.
The standard error is used to help you get a confidence interval for your coefficient values. We notice that the standard error of our variable 2.
The t value or t statistic is not a number we recommend you focus on. It is computed by dividing the coefficient by its standard error and is hard to interpret on its own. If you think about a coefficient and its standard error, you will see that the larger the coefficient is compared to its standard error, the more reliable it will be. This will indicate that the larger the t value, the more reliable the coefficient.
While the t value is not very helpful by itself, it is needed to compute a handy number — the P-value. The P-value is a really important and useful number and will be discussed next. The P-value indicates the probability that the estimated coefficient is wrong or unreliable. How small should the P-value be? That depends on a cut-off level that we decide on separately. This cut-off level is called the significance level. The cutoff selected depends on the nature of the data studied and the different error types.
Statistically speaking, the P-value is the probability of obtaining a result as or more extreme than the one you got in a random distribution. In other words, the P-value is the probability that the coefficient of the independent variable in our regression model is not reliable or that the coefficient in our regression output is actually zero! You will notice that the P-value of the TV spend variable in our example is very small.
We do not see a number after 4 decimals. Note that the P-value is similar in interpretation to the significance F discussed earlier in this book. The key difference is that the P-value applies to each corresponding coefficient, and the significance F applies to the entire model as a whole.
The coefficient of the independent variable is an estimate of the impact this variable has on the variable being studied. This is estimated from a sample that was analyzed in our regression analysis. So, if the interval does not contain 0, your P-value will be. What this indicates is that while we believe that the coefficient for TV ads in our example is Because this range does not include a zero, we have confidence that the TV ads spend does impact our sales results.
Data analysis using the regression analysis technique only evaluates the relationship between the variables studied. It does not prove causation. In other words, only the correlation aspect is evaluated. Causation is defined as the act of causing something.
Causation occurs when a change in one variable causes a change in the other variable. It is also referred to as a causal relationship. Causation is neither proved nor evaluated in a regression analysis. Instead, controlled studies where groups are split into two with different treatments are required to prove causation. Please remember that regression analysis is only one of the many tools in data analysis. Regression analysis is appropriate in many situations but not all data analysis situations.
Remember that regression analysis relies on sample data and reflects the relationship of the data in the sample. We assume that the sample reflects the true population, but this need not be so. Regression analysis is sensitive to outliers. Note: the assumptions of Linear Regression such as homoscedasticity, normal distribution of error terms, a linear relationship between the dependent and independent variables are not required here. Predicting the weather: you can only have a few definite weather types.
Stormy, sunny, cloudy, rainy and a few more. Medical diagnosis: given the symptoms predicted the disease patient is suffering from. Credit Default: If a loan has to be given a particular candidate depend on his identity check, account summary, any properties he holds, any previous loan, etc. HR Analytics: IT firms recruit a large number of people, but one of the problems they encounter is after accepting the job offer many candidates do not join.
So, this results in cost overruns because they have to repeat the entire process again. Elections: Suppose that we are interested in the factors that influence whether a political candidate wins an election. The predictor variables of interest are the amount of money spent on the campaign and the amount of time spent campaigning negatively. Discriminant Analysis is used for classifying observations to a class or category based on predictor independent variables of the data.
Discriminant Analysis creates a model to predict future observations where the classes are known. They make predictions upon the probability that a new input dataset belongs to each class. The class which has the highest probability is considered as the output class and then the LDA makes a prediction. They also make use of the probability of each class and also the data belonging to that class:. This method is used to solve the problem of overfitting of the model which arises due to the model performing poorly on test data.
This model helps us to solve the problem by adding an error term to the objective function to reduce the bias in the model. In L1 regularization we try to minimize the objective function by adding a penalty term to the sum of the absolute values of coefficients.
This is also known as the least absolute deviations method. It takes the minimum absolute values of the coefficients. It is generally used when we have more number of features because it automatically does feature selection. In L2 regularization we try to minimize the objective function by adding a penalty term to the sum of the squares of coefficients. Ridge Regression or shrinkage regression makes use of L2 regularization. This model assumes the square of the absolute values if coefficient.
Lambda is the penalty term. So by changing the values of alpha, we are basically controlling the penalty term. Higher the values of alpha, bigger is the penalty and therefore the magnitude of coefficients is reduced. Value of alpha, which is a hyperparameter of Ridge, which means that they are not automatically learned by the model instead they have to be set manually.
A combination of both Lasso and Ridge regression methods brings rise to a method called Elastic Net Regression where the cost function is :. When working with regression analysis, it is important to understand the problem statement properly. If the problem statement talks about forecasting, we should probably use linear regression. If the problem statement talks about binary classification, we should use logistic regression.
Similarly, depending on the problem statement we need to evaluate all our regression models. To learn more such concepts, take up Data Science and Business analytics Certificate Courses and upskill today. Learn with the help of online mentorship sessions and career assistance. Remember Me! Great Learning is an ed-tech company that offers impactful and industry-relevant programs in high-growth areas.
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