Adjusted R² will increase (decrease) if a variable is added to the model that
has a coefficient with an absolute value of its t-statistic greater (less) than
1.0.
Could someone please explain why T-stat > or < 1 will determine, whether
Adjusted R² will increase or decrease.
Agam with increase in variable makes R² rise & that doesn’t makes the added variable significant, for the added variable to be significant Adj R² shall rise whose formula is {1 – (n – 1/n – k – 1)(1 – R²)}
Now, to check whether Adj R² will rise or fall upon adding a variable can also be checked via looking at the t-statistic of the co-efficient of each added variable.
If the t-stats for co-efficient of each added variable comes to be significant than those variables can we added as it has great explanatory power.
A t stat > 1 confirms that the added variable has great explanatory power & so it can be added.
I hope now you understand why T stat is crucial. Thank you!
Hi Naman,
Thank you for your response,
I understand everything you wrote, just wanted to understand why does “A t stat > 1 confirm that the added variable has great explanatory power”. I understand if T-stat is more than T-critical, and Null Hypothesis was { bĸ^=0 }, then it means Null Rejected and bĸ^ is Significant. But why the threshold of 1 w.r.t. T-Stat of coefficient each added variable that determines whether Adjusted R² will rise or fall.
Also does this mean by default, that T-critical for coefficient of each added variable will be 1 in Absolute terms, and any T-stat beyond this means the variable can be added due to significant explanatory power?
Yes Agam your 2nd para seems to be correct. Look, this is a new concept introduced this time & I haven’t done the new classes till now so not very sure about your 2nd para. I’ll revert to you once I do the class. Thank you!
Awesome Naman.
Thank You So Much.