T1_ Interpreting the results

Interpreting Linear Regression Results

1. Focus Questions

• What is the fit (goodness of fit)?

• Is there significance in the results?

2. Analyzing Fit

• R-squared Value: 0.37385

  • Represents the goodness of fit of the linear regression model, rather than indicating a correlation between variables.

  • Indicates that the independent variable, click-through rating, accounts for 37% of the variation in weekly sales.

  • The remaining 63% of variation in weekly sales can be attributed to other factors that are not included in the model, which may include variables such as customer demographics, market conditions, or seasonal trends.

• Interpretation of Fit:

  • A fit of 37% is categorized as weak on a scale of 0-100%. The grading for fit can be labeled as:

    • Weak: 0% - 39%

    • Moderate: 40% - 69%

    • Strong: 70% - 100%

  • This highlights the need to consider additional predictors or variables to improve the predictive power of the regression model.

3. Analyzing Significance

• Significance Measurement:

  • The goal is to achieve 95% certainty in the results, implying that we allow a 5% chance that the results are due to random chance.

• P-value Analysis:

  • The p-value is critical in assessing the significance of the results, specifically focusing on the p-value associated with the independent variable (click-through rating).

  • A low p-value (ideally 0.05 or below) indicates strong evidence against the null hypothesis, affirming that the independent variable is significantly influencing the dependent variable.

• Scientific Notation of P-value:

  • P-values may appear in scientific notation due to formatting constraints in data analysis software like Excel.

  • Example of conversion: If p = 1.5E-6, it translates to 0.0000015 when the decimal is moved six places to the left.

    • This calculated value is notably less than the threshold of 5%, indicating a high level of confidence (>99%) in the results, which leads to the conclusion that the click-through rating is significantly influential on weekly sales.

4. Null Hypothesis and Conclusion

• Null Hypothesis:

• States that there is no effect or significance of the independent variable on the dependent variable, in this case, implying that the click-through rating does not influence weekly sales.

• Outcome of Analysis:

  • Given that the p-value is less than 5%, we reject the null hypothesis.

  • This leads us to accept the alternative hypothesis, which posits that a significant relationship exists between click-through rating and weekly sales.

• Summary of Results:

  • The R-squared value of 0.37385 signifies a weak fit within the regression model, indicating limited explainability of the independence variable by the model.

  • The p-value being below 5% reinforces the conclusion that the click-through rating is a significant predictor in impacting weekly sales.

5. Future Considerations

• It is crucial to explore and identify additional variables that may influence the remaining 63% of variation in sales.

• Potential factors for future analysis could include:

  • Advertising spend and channel effectiveness

  • Customer engagement metrics

  • Economic factors such as consumer confidence index or unemployment rates

  • Seasonal buying trends or promotional effectiveness.