Simple Linear Regression Calculator

Simple Linear Regression Formula:

\[ b = \frac{cov(x,y)}{var(x)} \] \[ a = \bar{y} - b\bar{x} \]

Regression Equation:

Slope (b):

Intercept (a):

Covariance (cov):

Variance of X (var):

Mean of Y (mean_y):

Mean of X (mean_x):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Simple Linear Regression?

Simple linear regression is a statistical method that models the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable (x), and the other is considered to be a dependent variable (y).

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ b = \frac{cov(x,y)}{var(x)} \] \[ a = \bar{y} - b\bar{x} \]

Where:

\( b \) — Slope of the regression line
\( a \) — Y-intercept of the regression line
\( cov(x,y) \) — Covariance between x and y
\( var(x) \) — Variance of x
\( \bar{y} \) — Mean of y values
\( \bar{x} \) — Mean of x values

Explanation: The slope (b) represents how much y changes for each unit change in x, while the intercept (a) represents the predicted y value when x is zero.

3. Importance of Linear Regression

Details: Linear regression is widely used for prediction and forecasting, understanding which factors are important in explaining the dependent variable, and identifying the strength of relationships between variables.

4. Using the Calculator

Tips: Enter comma-separated values for both x and y variables. Ensure both lists have the same number of values. The calculator will automatically compute all regression statistics.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between correlation and regression?
A: Correlation measures the strength of association between variables, while regression describes how one variable numerically depends on another.

Q2: How many data points do I need?
A: While you can calculate regression with as few as 2 points, more data points provide more reliable results.

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

Q4: How do I interpret the slope coefficient?
A: The slope represents the expected change in the dependent variable for a one-unit change in the independent variable.

Q5: What is R-squared?
A: R-squared measures the proportion of variance in the dependent variable that's explained by the independent variable (not shown in this simple calculator).