I have the following model: ln(MPG_{i}) = \beta _{0} + \beta *{1}WEIGHT*{i} + \beta *{1}FOREIGN*{i} + \beta *{3}FOREIGN*{i} * WEIGHT_{i} + \varepsilon_{i,j}

I want to use the **test** command to test whether the coefficient on $\beta_{3} >0.5$ in STATA.

I have used the following code and obtain this result:

test 1.foreign#c.weight = 0.5001

( 1) 1.foreign#c.weight = .5001

```
F( 1, 70) = 4.9e+07
Prob > F = 0.0000
```

So we reject our null, since the p-value is very small.

But the problem is that this for a two-tailed test.

My goal is to get the t-test value for this left-tailed test and then to store it. And then use the t-test to compute its p-value.

After computing the p-value, I decide whether or not to reject the null. I am certain that I would reject the null and the p-value would be quite small. Just need some help in figuring out how to code it the right way.

**EDIT:** I have tried using these commands:

```
lincom _b[forweight] - 0.5
display invttail(71, 0.5)
```

The last command spits out a value of 0. Now is this the p-value of the left-sided t-test?

Answer:

This is covered in this FAQ.

Here's the relevant code for testing that a coefficient is 0.5:

```
sysuse auto, clear
gen ln_mpg = ln(mpg)
regress ln_mpg i.foreign##c.weight
test _b[1.foreign#c.weight]=.5
local sign_wgt = sign(1.foreign#c.weight)
display "Ho: coef <= 0.5 p-value = " ttail(r(df_r),`sign_wgt'*sqrt(r(F)))
display "Ho: coef >= 0.5 p-value = " 1-ttail(r(df_r),`sign_wgt'*sqrt(r(F)))
```

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