Calculator Suite

Linear Regression Calculator

Perform simple linear regression analysis with comprehensive diagnostics and assumption checking

Analysis Settings
Data Input Method
Choose how to input your regression data

Select manual entry or use a sample dataset

Manual Data Entry
Enter X,Y pairs separated by commas, one pair per line

Format: X,Y (one pair per line). Example: 1,2.5

Label for the independent variable

Label for the dependent variable

Analysis Options
Configure regression analysis settings

Confidence level for intervals and tests

Display Options

Display confidence intervals around regression line

Identify potential outlier points

Quick Start
Load sample datasets to explore regression analysis
Sales vs AdvertisingIce Cream Sales vs TemperatureStudy Hours vs Test Scores

Educational Resources

Regression Formulas
Key formulas for simple linear regression analysis

Regression Equation

y=b0+b1x+ϵy = b_0 + b_1x + \epsilon

b0b_0 = y-intercept

b1b_1 = slope coefficient

ϵ\epsilon = error term

Slope Formula

b1=∑(xi−xˉ)(yi−yˉ)∑(xi−xˉ)2b_1 = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sum(x_i - \bar{x})^2}

Y-Intercept Formula

b0=yˉ−b1xˉb_0 = \bar{y} - b_1\bar{x}

R-squared

R2=SSregSStot=1−SSresSStotR^2 = \frac{SS_{reg}}{SS_{tot}} = 1 - \frac{SS_{res}}{SS_{tot}}

Proportion of variance explained by the model

Understanding Regression

Linear Regression

Models the relationship between a dependent variable (Y) and an independent variable (X) using a straight line that minimizes the sum of squared residuals.

Key Assumptions

  • • Linearity: Relationship is linear
  • • Independence: Observations are independent
  • • Homoscedasticity: Constant variance
  • • Normality: Residuals are normally distributed

Interpretation Guide

Slope: Change in Y per unit change in X
R²: Percent of variance explained
P-value: Statistical significance
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