Simple & Multiple Linear Regression Analysis

Construct Ordinary Least Squares predictive models, evaluate R-squared goodness-of-fit, test coefficient significance, assess VIF multicollinearity, and analyze diagnostic residuals.

What is Linear Regression Analysis?

Linear Regression Analysis models linear statistical relationships between a continuous dependent outcome variable (Target Y) and one or more independent continuous predictor variables (Predictors X1, X2, X3...). Regression modeling estimates predictor effect magnitudes, tests research hypotheses, and predicts future outcome values.

The module computes Ordinary Least Squares (OLS) regression parameters, model goodness-of-fit (R-squared, Adjusted R-squared, RMSE), coefficient t-test significance, Variance Inflation Factors (VIF) for multicollinearity, and renders full model diagnostic scatter charts.

Key Concept

Regression slope coefficients (b) represent the unit change expected in the target outcome variable for every 1-unit increase in a predictor variable, holding all other included predictor variables constant.

Data Layout Requirements

Data should be provided in tabular format containing an observation identification column, one target outcome metric column (Y), and one or more predictor metric columns (X).

Observation_ID	Predictor_X1	Predictor_X2	Predictor_X3	Outcome_Y
Obs_01	18.20	45.80	8.50	124.50
Obs_02	23.40	56.10	11.20	145.80
Obs_03	15.50	38.90	7.10	112.90
Obs_04	18.90	47.20	8.80	126.80

Example structure for Simple and Multiple Linear Regression Analysis.

Statistical Principles & Metrics

Regression concepts are defined through OLS optimization and diagnostic metrics:

Regression Slope Coefficient (b): Estimated change in target outcome Y for a one-unit change in predictor X, holding other predictors constant.
Coefficient of Determination (R2): Proportion of total variance in outcome Y explained by the model predictors (0.0 to 1.0, or 0% to 100%).
Adjusted R-squared: R-squared metric adjusted for the number of predictors relative to sample size, penalizing redundant variables.
Variance Inflation Factor (VIF): Measures how much coefficient variance is inflated due to collinearity among predictors. VIF > 5.0 indicates significant multicollinearity.

Residual Assumptions

Ensure that model residuals satisfy OLS assumptions: linearity, homoscedasticity (equal residual variance), independence, and normal distribution of residual errors.

Key Features of the DATES Module

Comprehensive Coefficient Table

Displays slope estimates, standard errors, t-statistics, p-values, 95% confidence bounds, and VIF scores for all predictor terms.

Model ANOVA & R2

Computes Regression ANOVA F-test, R-squared, Adjusted R-squared, and Root Mean Square Error (RMSE).

Diagnostic Scatter Plots

Renders Residuals vs Fitted values, Normal Q-Q plots, and Cook's Distance charts for outlier detection.

References & Citation

If you use DATES for Linear & Multiple Regression Analysis in your research, please cite:

@book{draper1998applied, title={Applied regression analysis}, author={Draper, Norman R and Smith, Harry}, year={1998}, publisher={John Wiley \& Sons} }