In the context of the regression model:

$\text{rdintens} = \beta_0 + \beta_1 \text{sales} + \beta_2 \text{salessq} + \beta_3 \text{profmarg} + \epsilon$

where the variables are as follows:

• rdintens: Research and development (R&D) intensity, or R&D as a percentage of sales,
• sales: Total sales in billions,
• salessq: The square of the sales variable (sales$^2$),
• profmarg: Profit margin, or profits as a percentage of sales,

we see that the coefficients $\beta_0$, $\beta_1$, $\beta_2$, and $\beta_3$ are not statistically significant after applying influential observation elimination and Least Absolute Deviation (LAD).

This lack of statistical significance suggests several possible inferences:

1. Weak Relationship: The variables sales, salessq, and profmarg may not have a strong predictive relationship with rdintens. This implies that changes in sales or profit margin may not significantly explain the variation in R&D intensity.

2. Model Specification Issues: The inclusion of sales and salessq may lead to multicollinearity, as these two variables are mathematically related. Multicollinearity can inflate standard errors, making it more challenging to detect significant coefficients.

3. Influence of Outliers: The use of influential observation elimination indicates that certain data points may have disproportionately affected the model’s initial estimates. The presence of such influential observations suggests variability in the data that could disrupt the model's ability to find significant predictors.

4. High Variability in R&D Intensity: If rdintens shows high variability that is not well-explained by sales or profit margin, it could indicate that other factors—such as industry type, firm strategy, or other non-financial metrics—play a more significant role in determining R&D intensity.

5. Sample Size and Power: A lack of statistically significant results might also stem from a small sample size or insufficient power in the data. If the dataset is limited or not representative, it could lead to non-significant estimates for the coefficients.

Conclusion

The lack of significance suggests that the chosen financial predictors may not be strong or reliable indicators of R&D intensity, or that the model needs further refinement, possibly by including other relevant variables or addressing multicollinearity issues. Additionally, robust estimation methods (like LAD) typically reduce the impact of outliers, so the issue likely lies with the predictors or model structure rather than solely with influential observations.

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Would you like more detailed explanations on any specific point, or do you have questions about the model?

Related Questions:

1. How does multicollinearity affect statistical significance in regression models?
2. What are alternative methods to address multicollinearity in regression?
3. How can we identify and interpret influential observations in regression analysis?
4. Why might Least Absolute Deviation be preferred over ordinary least squares in some cases?
5. What other factors could influence rdintens beyond sales and profit margin?

Tip:

When coefficients are not significant, examining the correlation between predictors and testing for omitted variables can help refine the model's structure.