we are having the following problem:
Suppose a linear regression model with the following form
$$ Y = B_0 + B_1 X_1 + B_2 X_2 + e$$
if we run the regression (with OLS) we end up with the following results
| $$X_i$$ | Estimation $$(B_i)$$ | Standard deviation |
|---|---|---|
| 1 | 0.85*** | (0.12) |
| 2 | 0.82*** | (0.26) |
where *** means p-value<0,001
The question that we are having with our team is the next:
Can we say this? $$B_1 > B_2$$
Since $$.85 > .82$$
or do we have to take into consideration the standard deviation? reason for which we couldn't assume the previous result.
The possible answer that we are thinking of are:
With the evidence we can't say that B1>B2 since if we have into account the standard deviation the CI overlaps
We can say that, on average, B1>B2, but is not statistically significant
On average, B1>B2
Other option/procedures...
Thank you in advance, if it is possible, it would help any paper that justifies the answer