matchResponse

Fit a linear regression model and find a set of predictor values that yields a specific response value according to the model.

Load the carbig data set, which contains measurements of cars made in the 1970s and early 1980s. Create a table that contains the acceleration, weight, and displacement predictors, and the miles per gallon response variable.

rng(0,"twister")  % For reproducibility
load carbig
tbl = table(Acceleration,Weight,Displacement,MPG);

Fit a linear regression model by using fitlm.

mdl = fitlm(tbl,"MPG");

Find the set of predictor values that corresponds to a predicted MPG value of 30.

vals = matchResponse(mdl,30)

vals=1×4 table
    Acceleration    Weight    Displacement    MPG
    ____________    ______    ____________    ___

       13.692       1994.9       122.36       30 

The model predicts that a car with an Acceleration value of 13.7, Weight value of 1995, and Displacement value of 122.4 has an MPG value of 30.

Fit a linear regression model and find the predictor values in a localized region that yield a specified response value according to the model.

Load the hald data set. Create a table containing the response variable, which is the heat evolved during hardening of a cement mixture, and the first two predictors, which are the amount of tricalcium aluminate and tricalcium silicate in the mixture.

rng(0,"twister")  % For reproducibility
load hald
X = ingredients(:,1:2);
tbl = array2table([heat X],VariableNames=["heat" "x1" "x2"]);

Fit a linear regression model by using fitlm.

mdl = fitlm(tbl,"heat");

Find a set of predictor values in the localized region [5 ≤ x1 ≤ 10, 30 ≤ x2 ≤ 40] that corresponds to a predicted heat value of 80.

vals = matchResponse(mdl,80,LowerBounds=[5 30],UpperBounds=[10 40])

vals=1×3 table
      x1        x2      heat
    ______    ______    ____

    5.0016    30.319     80 

The model predicts a heat value of 80 for x1 = 5 and x2 = 30.3.

Fit a linear regression model and find a set of categorical and continuous predictor values that yields a specific response value according to the model.

Load the patients data set, which contains simulated data for 100 hospital patients.

load patients

Convert the Gender and Smoker predictors to categorical.

Gender = categorical(Gender);
Smoker = categorical(Smoker);

Create a table containing the Age, Gender, Smoker, Weight, and Diastolic predictors.

tbl = table(Age,Gender,Smoker,Weight,Diastolic);

Fit a linear regression model to the Diastolic predictor using fitlm.

mdl = fitlm(tbl);

Find a set of predictor values that corresponds to a Diastolic value of 80, subject to the constraints that the patient is a male between the ages of 40 and 50, who weighs between 150–200 pounds. In this case, Global Optimization Toolbox is required because the Smoker predictor is categorical and its value is not fixed. If you have Global Optimization Toolbox, you can uncomment the lines below.

% vals = matchResponse(mdl,80,LowerBounds=[40,150], ...
%    UpperBounds=[50,200],CategoricalValues={"Male" []})

If you do not have Global Optimization toolbox, you can instead perform separate searches for a set of predictor values when Smoker=false and Smoker=true.

vals = matchResponse(mdl,80,LowerBounds=[40,150], ...
UpperBounds=[50,200],CategoricalValues={"Male" categorical(false)})

vals=1×5 table
    40.3028    Male    false    180.7239    80.0000

The model predicts that a 40-year old, nonsmoker male weighing 180 pounds has the target response value of 80.

Find the predictor values when Smoker=true.

vals = matchResponse(mdl,80,LowerBounds=[40,150], ...
UpperBounds=[50,200],CategoricalValues={"Male" categorical(true)})

Warning: Exact target value was not matched. Predictor bounds or values may need to be adjusted, or the target may be infeasible for the model.

vals=1×5 table
    40.0000    Male    true    150.0000    89.8196

The function issues a warning because it cannot find a predicted response that matches the target value when Smoker=true.