Different R2 from fitlm model from what I get from Ms. Excel linest model and SST not equal to SSE + SSR

Hello everyone,

I have created regression model of the form y~x1+x2+x3 using the fitlm function. However, the R2 predicted from the model is very different from what I get from Excel when i fit the same model using the Linest function in excel. Secondly I have noted that the fitlm function in matlab returns SST, SSE, and SST values that do not meet the statistical requirement of "SST = SSE + SSR". What could be the cause of this? Below is part of the code I am using in Matlab.

mdl_SI = fitlm(GNTables{k}(:,end-3:end),'Intercept',false);

ModelCoeff{k} = mdl_SI.Coefficients;

SSE = mdl_SI.SSE

SSR = mdl_SI.SSR

SST = mdl_SI.SST

mdl_SI.Rsquared

Any help will be grately appreciated.

Martin

[dpb]

load carsmall
X = [Weight,Horsepower,Acceleration];
mdl = fitlm(X,MPG)

mdl = 
Linear regression model:
    y ~ 1 + x1 + x2 + x3

Estimated Coefficients:
                    Estimate        SE          tStat        pValue  
                   __________    _________    _________    __________

    (Intercept)        47.977       3.8785        12.37    4.8957e-21
    x1             -0.0065416    0.0011274      -5.8023    9.8742e-08
    x2              -0.042943     0.024313      -1.7663       0.08078
    x3              -0.011583      0.19333    -0.059913       0.95236


Number of observations: 93, Error degrees of freedom: 89
Root Mean Squared Error: 4.09
R-squared: 0.752,  Adjusted R-Squared: 0.744
F-statistic vs. constant model: 90, p-value = 7.38e-27

[mdl.SSE mdl.SSR mdl.SST mdl.SSE+mdl.SSR]

ans = 1×4

1.0e+03 * 1.4888 4.5160 6.0048 6.0048

mdl.SSE+mdl.SSR==mdl.SST

ans = logical
   0

mdl.SST-(mdl.SSE+mdl.SSR)

ans = -9.0949e-13

The difference is in floating point rounding and is not significant either numerically nor statistically.

Now don't fit an intercept term...

mdl = fitlm(X,MPG,'intercept',false)

mdl = 
Linear regression model:
    y ~ x1 + x2 + x3

Estimated Coefficients:
           Estimate        SE        tStat       pValue  
          __________    _________    ______    __________

    x1    -0.0063238    0.0018485    -3.421    0.00094014
    x2      0.088238     0.035877    2.4595      0.015826
    x3        2.1221      0.14315    14.824    6.9409e-26


Number of observations: 93, Error degrees of freedom: 90
Root Mean Squared Error: 6.71

[mdl.SSE mdl.SSR mdl.SST mdl.SSE+mdl.SSR]

ans = 1×4

1.0e+03 * 4.0484 4.4879 6.0048 8.5364

Now the model doesn't meet the needs of a full linear model -- and you note fitlm doesn't even try to compute the overall statistics including Rsq because they no longer apply.

Likely Excel doesn't pay attention to such niceties if it does return Rsq for such a model if it even can estimate one without the intercept term; I'm not about to go try to dig into that in a MATLAB forum.

(BTW, this thread was a smart link to another I happened to respond to that had no response -- on investigation it seemed worth noting the cause for the record)