If one of the t-values (and its SE Coef) was erased from the output below, how could you still determine its value, from other output shown?
Output:
The regression equation is Cons = 29.6 + 0.95 Price + 0.777 Temp - 0.0691 TempPrice
Predictor Coef SE Coef T P
Constant 29.59 51.03 0.58 0.568
Price 0.955 5.648 0.17 0.867
Temp 0.7773 0.8778 0.89 0.386
TempPrice -0.06908 0.09707 -0.71 0.485
S = 7.50216 R-Sq = 24.9% R-Sq(adj) = 13.6%
Analysis of Variance
Source DF SS MS F P
Regression 3 372.98 124.33 2.21 0.119
Residual Error 20 1125.65 56.28
Total 23 1498.63
Source DF Seq SS
Price 1 198.38
Temp 1 146.09
TempPrice 1 28.51
I know $t=\frac{parameterEstimate}{SE(parameter)}$ ; however, since $SE(parameter)$ is removed, I'm not sure how to recalculate it.
In simple linear regression, $t=\sqrt{F}$ ; however this regression model has 3 predictors, so I don't think that relationship holds anymore.
I also thought to find the t-stat from a t-table, since I know the p-value. However, here the p-values are all very high, and the degrees of freedom for the test is 20, so the sample t-table doesn't go that high. Besides, that seems more of a hack than an actual answer.
Also, I know that in simple linear regression, $stderr(b_1)=\frac{s}{\sqrt{Sxx}}$ ; but, again, I don't think this is applicable to multiple regression.