NonLinearModel
statistics: NonLinearModel
Nonlinear regression model class.
A NonLinearModel object holds a nonlinear regression fitted by
fitnlm, together with its coefficients, fit statistics, and methods
for inference, prediction, and diagnostics. Construct one with
fitnlm, which documents the accepted inputs and
Name/Value pairs.
The estimated coefficients and their statistics are in the
Coefficients table; Rsquared, ModelCriterion,
LogLikelihood, RMSE, SSE, SST, and SSR
summarize the fit. The methods predict, feval, random,
coefCI, coefTest, plotResiduals, plotDiagnostics,
and plotSlice operate on the fitted model.
The fit statistics follow MATLAB’s conventions. SSE is the residual
sum of squares, SST the total sum of squares of the response about its
(weighted) mean, and SSR the regression sum of squares of the fitted
values about that mean; because the model is nonlinear, SST does
not in general equal SSR + SSE. Rsquared.Ordinary is
1 - SSE / SST and Rsquared.Adjusted corrects for
the error degrees of freedom. RMSE is sqrt (MSE), and
the Gaussian LogLikelihood uses the maximum-likelihood error variance
SSE / n. The information criteria in ModelCriterion
(AIC, AICc, BIC, CAIC) count the p
coefficients as the only parameters – the error variance is not
counted. coefTest is a Wald test: for a contrast matrix H it
forms (H*b)' * inv (H*V*H') * (H*b) / r
with V the coefficient covariance and r the number of rows of
H, referred to an F distribution on r and DFE
degrees of freedom. The summary printed by disp instead reports an
F statistic versus the zero model, formed from the uncorrected
regression sum of squares (the sum of the squared fitted values).
See also: fitnlm, nlinfit, nlparci, nlpredci, LinearModel, GeneralizedLinearModel
Source Code: NonLinearModel
The NonLinearModel class contains the following properties:
A table with one row per coefficient, its row names taken from
CoefficientNames, and the variables Estimate,
SE, tStat and pValue. tStat is the
estimate divided by its standard error and pValue is the
two-sided t test of a zero coefficient on DFE degrees
of freedom. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A cell array of character vectors with one name per coefficient, in
the order the model function expects them. The names default to
'b1', 'b2' and so on, unless fitnlm was given a
list of its own. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A square numeric matrix, one row and column per coefficient, holding
the estimated covariance of the estimates in Coefficients.
The square roots of its diagonal are the standard errors reported in
column SE of that table. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A positive integer counting the coefficients of the model, which is
the number of elements of the starting vector handed to
fitnlm. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A positive integer counting the coefficients estimated from the data.
A nonlinear fit estimates every coefficient it carries, so this equals
NumCoefficients. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A positive integer counting the predictor variables, that is the columns of the predictor matrix used for the fit. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A positive integer counting the observations used for the fit, after
the rows named by 'Exclude' and the rows carrying missing
values have been dropped. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A nonnegative integer, NumObservations less
NumCoefficients. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A positive scalar holding the estimated variance of the error term. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A positive scalar, the square root of MSE. This property is
read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A nonnegative scalar, the sum of the squared residuals weighted by the observation weights. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A nonnegative scalar, the weighted sum of squared deviations of the
response about its weighted mean. Because the model is nonlinear,
SST does not in general equal SSR plus SSE.
This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A nonnegative scalar, the weighted sum of squared deviations of the fitted values about the weighted mean of the response. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A scalar, the Gaussian log-likelihood at the estimates, formed with
the maximum-likelihood error variance SSE divided by
NumObservations. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A scalar structure with the fields AIC, AICc,
BIC and CAIC. All four count the coefficients as the
only parameters; the error variance is not counted. This property is
read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A scalar structure with the fields Ordinary and
Adjusted. Ordinary is one less the ratio of
SSE to SST, and Adjusted corrects that ratio
for the error degrees of freedom. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A table with one row per observation used for the fit and the
variables Raw, Pearson, Standardized and
Studentized. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A numeric column vector with one fitted value per observation used for the fit. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
Empty when the model was fitted by ordinary least squares. When
fitnlm was given a robust weight function, a scalar structure
whose field RobustWgtFun names it. This property is
read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A character vector showing the fitted model, built from the model function together with the coefficient names and the response name. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A character vector naming the response. It defaults to 'y'
for a fit from matrices and is the name of the response column for a
fit from a table. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A cell array of character vectors with one name per predictor. The
names default to 'x1', 'x2' and so on for a fit from
matrices, and are the column names for a fit from a table. This
property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
A cell array of character vectors holding PredictorNames
followed by ResponseName. This property is read-only.
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
The NonLinearModel class offers the following public methods:
NonLinearModel: mdl = NonLinearModel (data, resp, modelfun, beta0)
NonLinearModel: mdl = NonLinearModel (…, Name, Value)
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
NonLinearModel: yhat = predict (mdl, Xnew)
NonLinearModel: [yhat, yci] = predict (mdl, Xnew)
NonLinearModel: […] = predict (…, Name, Value)
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
NonLinearModel: yhat = feval (mdl, X)
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
NonLinearModel: ysim = random (mdl, Xnew)
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
NonLinearModel: ci = coefCI (mdl)
NonLinearModel: ci = coefCI (mdl, alpha)
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
NonLinearModel: [p, F, df] = coefTest (mdl)
NonLinearModel: […] = coefTest (mdl, H)
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
NonLinearModel: h = plotResiduals (mdl)
NonLinearModel: h = plotResiduals (mdl, plottype)
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
NonLinearModel: h = plotDiagnostics (mdl)
NonLinearModel: h = plotDiagnostics (mdl, plottype)
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
NonLinearModel: h = plotSlice (mdl)
Fit an exponential growth model y = b1 exp (b2 x) and inspect it.
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689
x = (1:10)'; y = [2.1; 2.9; 4.2; 5.3; 7.1; 9.4; 12.8; 16.5; 22.1; 29.8]; modelfun = @(b, x) b(1) .* exp (b(2) .* x); mdl = fitnlm (x, y, modelfun, [1; 0.3]); disp (mdl.Coefficients)
2x4 table
Estimate SE tStat pValue
________ __________ _______ ___________
b1 1.68375 0.0351945 47.8412 4.03037e-11
b2 0.286911 0.00235084 122.046 2.27082e-14
printf ("RMSE = %g, R^2 = %g\n", mdl.RMSE, mdl.Rsquared.Ordinary);
RMSE = 0.170943, R^2 = 0.999689