1. What is Simple Linear Regression?

Simple Linear Regression is a statistical method that models the relationship between a single independent variable and a dependent variable using a linear equation. It helps predict the value of the dependent variable based on the independent variable.

2. How Does the Calculator Work?

The calculator uses the Simple Linear Regression equation:

Where:

• \( \hat{y} \) — Predicted value of the dependent variable
• \( b_0 \) — Intercept (value of y when x = 0)
• \( b_1 \) — Slope (change in y per unit change in x)
• \( x \) — Independent variable value

Explanation: The equation establishes a straight-line relationship between the independent variable x and the predicted dependent variable ŷ.

3. Importance of Simple Linear Regression

Details: Simple Linear Regression is fundamental in statistical analysis, used for prediction, forecasting, and understanding relationships between variables in various fields including economics, biology, and social sciences.

4. Using the Calculator

Tips: Enter the intercept (b0), slope (b1), and the value of the independent variable (x). The calculator will compute the predicted value ŷ based on the linear regression equation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between simple and multiple linear regression?
A: Simple linear regression uses one independent variable, while multiple linear regression uses two or more independent variables to predict the dependent variable.

Q2: How is the slope coefficient interpreted?
A: The slope (b1) represents the change in the dependent variable for each one-unit change in the independent variable, holding other factors constant.

Q3: What assumptions does simple linear regression make?
A: Key assumptions include linearity, independence, homoscedasticity, and normality of residuals.

Q4: When is simple linear regression appropriate?
A: It's appropriate when there's a suspected linear relationship between two continuous variables and the data meets the regression assumptions.

Q5: How is the goodness of fit measured?
A: The coefficient of determination (R²) measures how well the regression line approximates the real data points (0-100% of variance explained).