Out of Sample/Scope Prediction with CI

[matt Mosh]

I need some help to get more details for Examples 2&3 to work
(page 7 in regress postestimation — Postestimation tools for regress ) https://www.stata.com/manuals/rregre...estimation.pdf.

I need to add a few independent variable observations after the regression and ANOVA analysis and then predict the prediction interval and individual value.

I used the following program to insert an observation into the dataset and prompt the user for an out of scope prediction:

capture program drop OutOfSamplePredict


program OutOfSamplePredict

*ask user for the out of sample dependent var
    display "This will create an out-of-sample prediciton..."
        display ""
    display "Please enter your Dependant variable, for the Y Axis:" _request(dependant)
        display "Thank you, to verify:"
        display "The Dependant variable selected, for the Y Axis, is:$dependant"
    display "Please enter the INDependant variable used for your regression - the X Axis:" _request(INDependant_var)
        display ""
        display "Thank you, to verify:"
        display "The InDependant variable you entered is:$INDependant_var"
        display ""
    display "Please enter the value you wish to predict,  (Dependent variable out-of-sample value):" _request(INDependant_value)
        display ""
    display "Thank you, to verify:"
    display "The value you want a prediciton for is: $INDependant_value"
    
*run the regression Quietly
    quietly regress $dependant $INDependant_var
    
* create a new observation
    quietly insobs 1
    
*insert the new Out of Sample observation that the user entered  into the INDependant variable 
    replace $INDependant_var = $INDependant_value in l

*create a local macro name to store the  prediciton value to.

    local mypred = _b[_cons] + _b[$INDependant_var]*$INDependant_value

    
    display "your linear prediction equation : " _b[_cons] " + " _b[$INDependant_var] " * " $INDependant_value 
        display ""
    display "prediction value is = `mypred'"
        display ""
    display "writing your values to the dataset..."
        
        
    predict predict, xb
    predict residuals, residuals
    predict CooksDistance, cooksd
    predict StandardResiduals, rstandard
    predict Leverage, leverage
    
* insert the prediction value based on the regression equation
    replace predict = `mypred' in l

    
    
* generate leverage for the predicted value
/*
    predict temp_leverage in l, leverage      /* because predict can only make new variables create a temp variable  */
    replace Leverage = temp_leverage in l     /* replace the only created value into the replacement variable */
    drop temp_leverage                        /* drop the temporary variable */
*/

* generate Cooks Distance for the predicted value
/*
    predict temp_cooks in l, cooksd      /* because predict can only make new variables create a temp variable  */
    replace CooksDistance = temp_cooks in l     /* replace the only created value into the replacement variable */
    drop temp_cooks                        /* drop the temporary variable */
*/    
* generate Standard Error for the predicted value

    predict SE_Forecast in l, stdf      
    predict SE_Predict in l, stdp
    predict SE_Residual in l, stdr
    
* generate the Confidence interval for the out of scope prediction
    local 2SD = SE_Forecast[_N] * 2
    local UCL = predict[_N] + `2SD'
    local LCL = predict[_N] - `2SD'
    
    display "The Upper bound for your Confidence Interval is: `UCL'" 
        display ""
    display "The LOWER bound for your Confidence Interval is: `LCL'" 


    



end

I followed the examples but I got a different answer than our instructor who used "R". This is their code and answer:

> new.amount <- data.frame(pectin=c(1.5))
> predict(model,newdata=new.amount,interval="predict ion")
fit lwr upr
1 62.5725 53.19595 71.94905

---

Dataset

* Example generated by -dataex-. To install: ssc install dataex
clear
input float firmness byte pectin
 46.9 0
 50.2 0
 51.3 0
56.48 1
59.34 1
62.97 1
67.91 2
70.78 2
73.67 2
68.13 3
70.85 3
72.34 3
end

[matt Mosh]

Never mind, I found and adapted a solution:

capture program drop OutOfSamplePredict


program OutOfSamplePredict

*ask user for the out of sample dependent var
    display "This will create an out-of-sample prediciton..."
        display ""
    display "Please enter your Dependant variable, for the Y Axis:" _request(dependant)
        display "Thank you, to verify:"
        display "The Dependant variable selected, for the Y Axis, is:$dependant"
    display "Please enter the INDependant variable used for your regression - the X Axis:" _request(INDependant_var)
        display ""
        display "Thank you, to verify:"
        display "The InDependant variable you entered is:$INDependant_var"
        display ""
    display "Please enter the value you wish to predict,  (Dependent variable out-of-sample value):" _request(INDependant_value)
        display ""
    display "Thank you, to verify:"
    display "The value you want a prediciton for is: $INDependant_value"
    
*run the regression 
     regress $dependant $INDependant_var
    
* create a new observation
    quietly insobs 1
    
*insert the new Out of Sample observation that the user entered  into the INDependant variable 
    replace $INDependant_var = $INDependant_value in l

*create a local macro name to store the  prediciton value to.

    local myY_Hat = _b[_cons] + _b[$INDependant_var]*$INDependant_value

    
    display "your linear prediction equation : " _b[_cons] " + " _b[$INDependant_var] " * " $INDependant_value 
        display ""
    display "prediction value is = `myY_Hat'"
        display ""
    display "writing your values to the dataset..."
        
        
    predict Y_hat, xb
    predict residuals, residuals
    predict CooksDistance, cooksd
    predict StandardResiduals, rstandard
    predict Leverage, leverage
    
* insert the prediction value based on the regression equation
    replace Y_hat = `myY_Hat' in l

    
    
* generate leverage for the predicted value
/*
    predict temp_leverage in l, leverage      /* because predict can only make NEW variables create a temp variable  */
    replace Leverage = temp_leverage in l     /* replace the only created value into the variable where you want predict to ADD an entry */
    drop temp_leverage                        /* drop the temporary variable */
*/



    
* generate the Confidence Interval and Prediction Interval for the out of scope prediction
    *help from https://www.ics.uci.edu/~jutts/110-201-09/StataForCIandPI.doc
    
    * generate Standard Errors for the predicted value

        predict PI_SE_Forecast in l, stdf      
        predict CI_SE_Predict in l, stdp
        predict SE_Residual in l, stdr
    *Generate the t-multiplier for a 95% interval and the appropriate degrees of freedom from the regression. 
        local tmult=invttail(e(df_r),.025)
    *Generate the lower and upper end points for each interval
        generate lowerCI = Y_hat - `tmult'*CI_SE_Predict
        generate upperCI = Y_hat + `tmult'*CI_SE_Predict
        generate lowerPI = Y_hat - `tmult'*PI_SE_Forecast
        generate upperPI = Y_hat + `tmult'*PI_SE_Forecast

    
    
    display "The Prediction Interval for the point you entered is:" 
        list Y_hat lowerPI upperPI in l, clean
        display "This corresponds to the range that a new  observation would fall inbetween 95% of the time. "
        display ""
        display ""
    display "The Confidence Interval for the point you entered is: " 
        list Y_hat lowerCI upperCI in l, clean
        display "This corresponds to the Average that a new set of observations would fall inbetween 95% of the time. "
        display ""


    



end