Multiple Regression - Interpreting t-stat

#1
Hi all,

If the model fit is satisfactory (ie. R-squared value is sufficiently high), how should the t-stat be interpreted... my reading indicated that the following holds - could you please confirm.

1. The t-stat can be a measure of the relative strength of prediction (is more reliable than the regression coefficient because it takes into account error), and the generalisability of the findings beyond the sample.

2. A t-stat of greater than 1.96 with a significance less than 0.05 indicates that the independent variable is a significant predictor of the dependent variable within and beyond the sample.

3. The greater the t-stat the greater the relative influence of the independent variable on the dependent variable.

4. A t-stat of less than 1.96 with a significance greater than 0.05 indicates that the independent variable is NOT a significant predictor of the dependent variable BEYOND the sample. However, as the model is a good fit with the sample - it does not detract from its value within the sample... it only affects generalisability outside the sample.

Thanks,
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JohnM

TS Contributor
#2
Actually, I don't agree with any of the statements......

In regression, the t-stat, coupled with its p-value, indicates the statistical significance of the relationship between the independent and dependent variable. The p-value is not an indicator of the generalizability of the model (i.e., will it accurately predict "outside" of the model?), but the probability of getting the result if in fact the null hypothesis is true (i.e., "no significant relationship").

The generalizability of the model will be determined by how well you designed the study and the scientific merit of the theories and hypotheses, not by any of the statistical output.

Considering only the significant relationships between independent variables and the dependent variables, the ones with the highest amount of influence will generally be the ones that have the highest beta coefficients:

y = x0 + B1x1 + B2x2 + ... + Bnxn + e