This output is from a multiple linear regression analysis. Let’s break it down in sections:

1. Regression Statistics

• Multiple R (0.638376): This is the correlation coefficient, showing the strength of the relationship between the dependent variable and the independent variables. A value of 0.638 means a moderate positive correlation.
• R Square (0.407524): This indicates that about 40.75% of the variability in the dependent variable is explained by the model.
• Adjusted R Square (0.282792): This is adjusted for the number of predictors in the model, providing a more accurate estimate when dealing with multiple independent variables. It suggests a weaker fit than R² (28.28% of the variance explained).
• Standard Error (36.95796): This measures the average distance that the observed values fall from the regression line.
• Observations (24): The number of data points (24 observations) used in the regression.

2. ANOVA (Analysis of Variance)

• df (degrees of freedom):
  • Regression df = 4, corresponding to the number of predictors.
  • Residual df = 19, corresponding to the number of observations minus the number of predictors and the intercept.
  • Total df = 23, the total number of observations minus 1.
• SS (Sum of Squares):
  • Regression SS = 17850.58, representing the explained variability.
  • Residual SS = 25951.92, representing the unexplained variability.
  • Total SS = 43802.5, the total variability.
• MS (Mean Square):
  • Regression MS = 4462.644 (Regression SS / Regression df).
  • Residual MS = 1365.891 (Residual SS / Residual df).
• F-statistic (3.267204): This tests the overall significance of the model. A higher F-statistic indicates that the model is significant. The significance F value (p-value) is 0.033731, which is less than 0.05, indicating the model is statistically significant.

3. Coefficients

Each independent variable has an associated coefficient, standard error, t-statistic, and p-value. These values tell us about the influence of each variable on the dependent variable:

• Intercept (1794.919): This is the expected value of the dependent variable when all predictors are 0.
  • P-value (0.002498): This is significant (p < 0.05), indicating the intercept is statistically meaningful.
• Price (-0.02985): Suggests that for each unit increase in Price, the dependent variable decreases by 0.02985, although the p-value (0.946176) shows this is not statistically significant.
• Time-Free (-5.82049): Suggests a negative relationship, but it is not statistically significant (p = 0.245918).
• Income (-0.56466): Suggests a significant negative relationship (p = 0.012425), meaning Income has a meaningful negative impact on the dependent variable.
• South Bay (-0.09388): Suggests a small negative relationship, but it is not statistically significant (p = 0.633378).

Conclusion:

• The model explains 40.75% of the variability in the dependent variable.
• The overall model is statistically significant (p-value of 0.033731).
• Of the predictors, only Income has a statistically significant impact on the dependent variable.

Would you like to explore any details or have further questions?

Related Questions:

1. How do we interpret a high p-value for a coefficient in regression analysis?
2. What is the significance of the F-statistic in this regression model?
3. Can you explain the difference between R-Square and Adjusted R-Square?
4. How does the standard error affect the confidence intervals of the coefficients?
5. What does it mean when a coefficient is not statistically significant but the model is?

Tip:

Always check the p-values of individual predictors to understand which variables significantly contribute to the model.