One-side test

[kwangsooKo]

Dear sir

Hello. I’d like to ask a question about one-sided test.

I did hypothesis test as following.

1. Linear Regression
Return = constant + a1*return(1 lag) + a2*return(2 lag) + b1*flow(1 lag) + b2*flow(2 lag)
The coeff. are a1, a2, b1, and b2

2. one-sided test
H1: b1 + b2 < 0
To test the hypothesis " b1 + b2 < 0", I used " RESTRICT"
__________________________________
LINREG return
# Constant return{1 to 2} flow{1 to 2}

Restrict(form=f) 1
# 4 5
# 1 1 0
__________________________________
Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Constant 0.037908179 0.038312956 0.98943 0.32259713
2. RETURN{1} 0.012216603 0.024737433 0.49385 0.62147799
3. RETURN{2} -0.006143524 0.026467863 -0.23211 0.81647968
4. FLOW{1} 0.000030111 0.000045716 0.65866 0.51020732
5. FLOW{2} -0.000058185 0.000044107 -1.31920 0.18728884

t(1631)= 0.796219 or F(1,1631)= 0.633964 with Significance Level 0.42602075
___________________________________

RESTRICT is report a two-tailed t test in addition to the F test as shown.

So I have two questions.

First question: Sum of coeff. (coeff of Flow {1}+coeff of Flow{2) = -0.000014<0) for test is negqtive. But t -stat. is positive(= 0.796219>0)
I don't understand why this has different sign.

Secound question:
How can I interpret the results of the test as one-tailed t test ?
I interpret that the result means t(1631) = - 0.796219 with significance level 0.2130(= half of 0.42602075) as one-tailed t test .
Is it right?

Sorry for my pool English.
I'll be looking forward to your reply.
Thanks.

[TomDoan]

The reported t is just the square root of the F, so it won't be signed.

That's correct. If the test statistic is in the tail of interest, you multiply the reported significance level by .5. (If it's in the wrong tail, you multiply by .5 and subtract that from 1).