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model using fitlm .
beta = fitlm(data(:,2:5),data(:,1),...
'ResponseVar',variables(1,:),...
'PredictorVars',variables(2:5,:))
h e function fitlm uses a least mean-squares criterion to calculate beta . h e
output of the function fitlm
beta =
Linear regression model:
Perm ~ 1 + Poro + MaCo + TrFF + InPo
Estimated Coefficients:
Estimate SE tStat pValue
________ _______ ________ ________
(Intercept) 0.15868 7.5546 0.021005 0.98336
Poro 50.636 18.714 2.7058 0.010458
MaCo -330.9 150.51 -2.1986 0.034609
TrFF -0.17857 0.18537 -0.96329 0.34201
InPo -0.45263 0.50101 -0.90344 0.37247
Number of observations: 40, Error degrees of freedom: 35
Root Mean Squared Error: 2.68
R-squared: 0.483, Adjusted R-Squared 0.424
F-statistic vs. constant model: 8.18, p-value = 9.07e-05
i rst recalls the linear regression model using the names of the response
variable and the predictor variables. It then displays a table with the regression
coei cient estimates for each predictor variable in the i rst column, the
standard error, the t -statistic, and the p -values of the coei cient estimates.
h e quality of the model is good as the p -value of the constant model (i.e.,
with no inl uence of predictor variables on the response variable) is very low,
as the last line of the comments below the table suggests. h e p -values of the
individual regression coei cient estimates suggests that only the porosity and
matrix conductivity inl uence the permeability of the Sherwood Sandstone,
at a 5% signii cance level.
h ere are multiple ways to examine the quality of the result. h e Statistics
Toolbox includes several functions for displaying diagnostic plots to identify
and remove outliers from the data set. We can, for instance, produce a
leverage plot of the data and the model by typing
plotDiagnostics(beta)
h e leverage plot displays the leverage that an individual measurement has
when added to the regression model, assuming that all other measurements
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