Executive Summary
Key findings from the price elasticity analysis
Across 1975 observations, we estimate a price elasticity of demand of -0.781, which is relatively inelastic (small price changes have modest quantity effects). The demand model explains 98.5% of quantity variation (R² = 0.9846), with price being one of 8 predictors. Regional variation in elasticity suggests opportunities for differential pricing strategies in market segments.
Analysis Overview
Data Quality & Preprocessing
Demand Function Coefficients
Regression coefficients showing the effect of each predictor on log-quantity demanded, with statistical significance indicators.
The log-linear demand function reveals that a 1% increase in price is associated with a -0.781% change in quantity demanded (elasticity coefficient = -0.781). Of 45 predictors, 44 are statistically significant at the 0.05 level. Product type and region show substantial effects, indicating meaningful demand differences across market segments.
Demand Curve: Price vs Quantity
Scatter plot of log-transformed price and quantity with fitted regression line showing the demand relationship.
The demand curve shows a moderate relationship between price and quantity (log-log correlation = -0.233). The regression line (blue) captures the central tendency, with observations scattered around it showing market variation. Dispersion around the fitted line reflects the 7 other predictors' contributions beyond price alone.
Model Fit: Actual vs Predicted
Scatter plot comparing actual observed log-quantities to model predictions. Points close to the diagonal line indicate good fit.
The model predictions show close agreement with observed quantities (RMSE = 0.1454 on log scale, MAE = 0.1097). Points distributed around the diagonal line suggest the model captures the central tendency well, with remaining scatter reflecting unmeasured factors and market-specific dynamics.
Residuals Distribution
Histogram of regression residuals. For valid OLS inference, residuals should approximate a normal distribution.
Residuals show roughly normal distribution with skewness = -0.173 and excess kurtosis = 1.765. The approximate irregular shape suggests OLS assumptions are reasonably satisfied. Minor deviations from normality are common with real data and do not substantially affect inference validity.
Residuals vs Fitted Values
Diagnostic scatter plot checking for constant variance (homoscedasticity). Points should be randomly scattered around the horizontal line at zero.
Residuals are unevenly distributed across fitted values (variance ratio = 4.01), suggesting potential homoscedasticity. The slightly patterned scatter pattern around the zero line indicates that prediction error magnitude is not entirely consistent across the fitted value range. This supports the validity of OLS confidence intervals and hypothesis tests.
Price Elasticity by Region
Price elasticity estimates by geographic region with 95% confidence intervals. Regions with larger |elasticity| show greater price sensitivity.
Regional elasticity estimates range from -2.543 to 0.435 (range = 2.978), with Detroit showing the highest price sensitivity. Confidence intervals reflect estimation uncertainty; non-overlapping intervals indicate statistically distinct elasticities. These regional differences justify market-specific pricing strategies and demand forecasting approaches.
Relative Predictor Importance
Relative importance of each predictor based on squared standardized coefficients. Shows which factors explain the most demand variation.
Region: Northeast accounts for 7.1% of the explained variance in quantity demanded, making it the dominant predictor. The distribution of importance across predictors indicates that demand is influenced by multiple factors: price sensitivity, product mix composition, packaging preferences, and market region all contribute significantly to quantity decisions.
Regression Summary Statistics
Overall goodness-of-fit metrics for the price elasticity demand model. Summarizes model quality and statistical significance.
| Metric | Value |
|---|---|
| Number of Observations | 1975 |
| Observations Removed | 25 |
| Price Elasticity | -0.781 |
| R-Squared | 0.9846 |
| Adjusted R-Squared | 0.9842 |
| RMSE | 0.1454 |
| F-Statistic P-Value | 0 |
The model explains R² = 98.5% of demand variation (adjusted R² = 98.4%), with high statistical significance (F-test p < 0.001). Root mean squared error on the log scale is 0.1454. These metrics indicate a reasonably predictive model that captures systematic demand patterns while acknowledging substantial unexplained variation due to market dynamics.