Can we interpret the coefficients from Model B as a causal parameter? Are the pr

Question

Can we interpret the coefficients from Model B as a causal parameter? Are the predictors significant in Model B?

MODEL B

SUMMARY OUTPUT

MODEL A SUMMARY OUTPUT Regression Statistics Multiple R 0.97688814 R Square 0.954310437 Adjusted R Square 0.939080583 Standard Error 3.277208147 Observations 5 ANOVA df SS MS F Significance F Regression 1 672.9797203 672.9797203 62.66051004 0.00420315 Residual 3 32.22027972 10.74009324 Total 4 705.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.531468531 3.604616436 0.702285132 0.533086906 -8.940029729 14.00296679 -8.940029729 14.00296679 X Variable 1 3.43006993 0.433317283 7.915839187 0.00420315 2.051060943 4.809078917 2.051060943 4.809078917

Explanation / Answer

Just because the R squared and standard error are similar for both model A and model B we cannot interpret the coefficients from model B as a causal parameters

The predictors in model B are not significant because these is a possibility of the coefficients being zero

This can be inferred from the confidence interval hich contains zero value for all the coeffiecients and the constant for model B

Hence not significant

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