Plotting the slope

[Justine Borja]

Good day Statalisters!

Is there a command in Stata where I can plot a curve using the lower bound and upper bound slopes I have obtained from my results. The following are the slopes;

(1)
LB: -1.255755
UB: .486735
(2)
LB: -.616485
UB: .3723716

Hoping for y'all generous help

Thank you,
Justine

[Fei Wang]

Could you elaborate how the four numbers would be related to the curve?

[Justine Borja]

I am plotting for a U-shaped curve and I want to picture out the slopes using the obtained values of the lower bound and upper bound. The first LB and UB is not related to the second LB and UB. They are separate values, so I am aiming to visualize two different U-shaped curves.

[Bruce Weaver]

Hello Justine. How did you get the LB and UB values you show in #1? Can you illustrate with a small dataset (using -dataex- and code delimiters as described in the FAQ)? Thank you for clarifying.

[Fei Wang]

If I understand correctly, you'd like to plot a U-shaped curve whose slopes change from negative to positive and LB and UB are the min and max of the slopes. LB and UB cannot pin down a curve unless we know more information, including the domain, functional form of the curve, etc.

[Justine Borja]

Here are the information:

  utest lnOPEN lnOPEN2, min (3) max (5) fieller

Specification: f(x)=x^2
Extreme point:  4.441334

Test:
     H1: U shape
 vs. H0: Monotone or Inverse U shape 

-------------------------------------------------
                 |   Lower bound      Upper bound
-----------------+-------------------------------
Interval         |           3                5
Slope            |   -1.255755          .486735
t-value          |   -3.564232         2.831656
P>|t|            |    .0011936         .0057557
-------------------------------------------------

Overall test of presence of a U shape:
     t-value =      2.83
     P>|t|   =    .00576

95% Fieller interval for extreme point: [4.1507043; 4.7553174]

 utest lnOPEN lnOPEN2, min (3) max (5) fieller

Specification: f(x)=x^2
Extreme point:  4.246864

Test:
     H1: U shape
 vs. H0: Monotone or Inverse U shape 

-------------------------------------------------
                 |   Lower bound      Upper bound
-----------------+-------------------------------
Interval         |           3                5
Slope            |    -.616485         .3723716
t-value          |   -2.325283         2.518565
P>|t|            |    .0150794         .0099802
-------------------------------------------------

Overall test of presence of a U shape:
     t-value =      2.33
     P>|t|   =     .0151

95% Fieller interval for extreme point: [3.5129539; 4.6665431]

[Bruce Weaver]

The command you are using is this user-written command, I think:

ssc describe utest

[Fei Wang]

It seems you'd like to plot the relationship between y, x and squared x based on two different sets of coefficients. Below is an example (-utest- is unnecessary for the plot).

sysuse auto, clear

gen mpgsq = mpg^2
reg price mpg mpgsq gear_ratio if foreign == 0
utest mpg mpgsq
margins, predict(xb) at(mpg=0 mpgsq=0)
local a1 = _b[mpgsq]
local b1 = _b[mpg]
local c1 = r(table)[1,1]
sum mpg if e(sample)
local min1 = r(min)
local max1 = r(max)

reg price mpg mpgsq gear_ratio if foreign == 1
utest mpg mpgsq
margins, predict(xb) at(mpg=0 mpgsq=0)
local a2 = _b[mpgsq]
local b2 = _b[mpg]
local c2 = r(table)[1,1]
sum mpg if e(sample)
local min2 = r(min)
local max2 = r(max)

twoway function `a1'*x^2 + `b1'*x + `c1', range(`min1' `max1') || ///
       function `a2'*x^2 + `b2'*x + `c2', range(`min2' `max2')    ///
       ytitle("Predicted car price") xtitle("Miles per gallon")    ///
       leg(order(1 "Domestic cars" 2 "Foreign cars"))

[Justine Borja]

Can I use these codes directly? Thanks for your help Fei Wang, really appreciated.

[Fei Wang]

Can I use these codes directly? Thanks for your help Fei Wang, really appreciated.

Yes. But make sure to replace all variables in my example with yours.

[Justine Borja]

Hey it's me again Fei Wang, Do your codes work as well in ARDL? Because that is the estimation method I am using. And what do you mean on the "foreign==0"? I dont get it. Please clarify sir.

Thanks,
Justine