Applications of Regression Analysis

Applications of Regression Analysis

• Predicting outcomes based on input variables, such as predicting house prices based on size and location.
• Understanding trends over time, such as analyzing sales data to identify patterns.
• Predicting future values, like forecasting demand for products.

Limitations of Regression Analysis

• Assumption violations can lead to unreliable results.
• Overfitting occurs when a model is too complex and fits the training data too closely, leading to poor performance on new data.
• Linear relationship assumption may not always be true.

Examples of Regression Analysis

• Regression analysis can predict a student's test score based on study hours.
• Data is gathered on study hours and test scores, and regression analysis is used to find the best-fitting line.
• The line can be used to estimate a student's test score based on study time.

Types of Regression Analysis

• Simple Linear Regression: predicts a student's test score based on study hours.
• Multiple Linear Regression: predicts house prices based on size, location, and number of bedrooms.
• Polynomial Regression: predicts the price of gasoline based on time of year, using a curved line to fit the data.

Key Concepts

• Dependent Variable: the main thing being predicted, such as test scores or house prices.
• Independent Variable(s): factors that might affect the dependent variable, such as study hours or location.
• Coefficient: a number that shows how much the dependent variable changes when an independent variable changes.
• Intercept: the starting point or baseline value of the dependent variable.

Assumptions of Regression Analysis

• Linearity: the relationship between independent and dependent variables should be linear.
• Independence: observations should be independent of each other.
• Homoscedasticity: residuals should have constant variance.