Regression is a complex topic, but before I explain it mathematically, I’ll give you some real-world examples. Regression analysis is used in a variety of real-world situations, including predicting salary based on years of experience, predicting exam scores based on study hours, predicting resale price based on vehicle age, and so on.
Thus, based on the examples provided above, we can conclude that regression analysis is a technique for analyzing relationships between variables in order to gain a better understanding of our surroundings. Regression analysis is a statistical method for analyzing data. To predict future outcomes, data is analyzed in a variety of fields, including economics, social sciences, and finance. As a result, regression analysis is one of the most commonly used statistical techniques for data analysis.
What is Regression Analysis?
Regression analysis is a statistical tool or technique used to analyze the relationship between two variables. The two variables used in the regression method are known as the dependent variable (X) and the independent variable (Y). The regression analysis method helps predict and understand the relationship between two variables i.e. X and Y. The dependent variable (X) is also known as the “outcome variable” while the independent variable (Y) is known as the “predictor variable”. The dependent variable (X) is the main outcome that we want to predict, while the independent variable (Y) is something that influences the outcome, i.e. the dependent variable (X). There are numerous applications for regression analysis. Longitudinal studies allow us to investigate how early life circumstances or characteristics relate to outcomes in adulthood, middle age, and later life.
For example, we could investigate whether there is a clear correlation between academic performance and life satisfaction in middle age. Using a scatter plot, we can compare the life satisfaction of the members of our sample with their average academic performance. We can see that there is a pattern.
But can we tell how much more life satisfaction people can expect if they score one point higher on average at school? What would it be like if they had half a grade point less on average? We can summarise the data in the graph by drawing a line that goes roughly through the middle of all the data points.
There is a black line that denotes a regression line that we can use to estimate or model the relationship between our independent and dependent variables. Using this model, we can predict that someone with a grade point average of 2.5 would have a life satisfaction score of approximately 7.6 out of 10. This is on average about 0.8 lower than someone with a grade point average of 3.5, whose life satisfaction would be about 8.4 out of 10. It is important to remember that the line is just an estimation and will not predict the outcome perfectly.
Types of Regression Analysis
Various scenarios involve complex data. Therefore, it can be a challenge to accurately predict and understand the relationship between the variables. Therefore, different types of regression analysis serve different purposes.
- Linear Regression: This is one of the simple and widely used regression analysis methods. The method of assessing a linear relationship between dependent and independent variables is simply known as linear regression.
- Multiple Regression: Multiple regression is similar to linear regression, In the linear regression method, there will be a single independent variable while in the multiple regression method, there will be multiple independent variables influencing the dependent variable.
- Polynomial Regression: Polynomial regression is the opposite of linear regression. In this method, the relationship between dependent and independent variables is defined by a curve instead of a straight line.
- Logistic Regression: Logistic regression is used to predict two outcomes i.e. if the dependent variable has only two possible outcomes, the logistic regression method is used.
- Ridge Regression and Lasso Regression: Ridge regression and lasso regression techniques are used in the linear regression method to manage the overfitting in predictive models and thus improve the model’s predictive performance.
- ElasticNet Regression: ElasticNet Regression is a combination of Ridge and Lasso regression methods that are used to balance their strengths to improve model performance.
Each type of regression helps to predict or forecast intended results using different patterns in the data.
Regression Analysis: Formulas
1. Simple linear regression: Y = a + bX, where
Y is the dependent variable
X is the independent variable
a is the intercept (the value of Y when X = 0).
b is the slope (the change in Y for a one-unit change in X).
2. Multiple linear regression: Y = a + b₁X₁ + b₂X₂ + … + bₙXₙ, where
Y is the dependent variable.
X₁, X₂, …, Xₙ are the independent variables.
a is the intercept.
b₁, b₂, …, bₙ are the coefficients of the independent variables.
3. Non-linear regression: Y = f(X,θ), where
Y is the dependent variable
X is the independent variable(s)
θ represents the parameters of the non-linear function f.
Regression Analysis: Examples
Regression analysis is used in different contexts. Some of the examples of regression analysis used in various fields are as follows.
1. Economics
- Predicting House Prices: Assume you want to forecast house prices based on variables such as size, number of bedrooms, location, etc. You would use a multiple regression analysis to predict the price (dependent variable) based on a variety of independent variables such as square footage, number of bedrooms, neighborhood, and so on.
2. Marketing
- Sales Forecasting: Businesses frequently use regression analysis to forecast sales. They may use historical sales data (dependent variable) in conjunction with factors such as advertising expenditure, seasonality, economic indicators, and so on (independent variables) to forecast future sales.
3. Healthcare
- Examining Health Factors: In healthcare, regression analysis can be used to understand the relationship between a specific health outcome (for example, blood pressure) and a variety of factors such as age, diet, exercise frequency, and so on. This helps identify which factors might influence the health outcome.
4. Finance
- Credit Scoring: Financial institutions use logistic regression to determine credit risk. They use factors such as income, credit history, debt-to-income ratio, and so on to predict whether a borrower will default on a loan or not (a binary outcome).
5. Education
- Student performance: Regression analysis can be used to predict student’s performance based on various factors such as attendance, study time, scores, etc.
These examples show how regression analysis is used in various industries to understand relationships between variables, make predictions, and support decision-making processes.
Conclusion
The fundamental mathematical and statistical knowledge is important in understanding regression analysis as it serves as the foundation for more advanced concepts in machine learning and artificial intelligence.
Regression analysis is one of the most valuable tools for analyzing and predicting certain outcomes based on data patterns. It is one of the most useful statistical tools for making data-driven decisions and predicting future outcomes. Many industries often use regression analysis to manage financial risk and estimate future values.
Leave feedback about this