MSE Residuals standard error lm Model

Author

Mudry STater

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library(glmnet)

Le chargement a nécessité le package : Matrix

Loaded glmnet 4.1-4

train=sample(32,25,replace = T)
train

 [1]  5 16 32  4  1 21 11 13 10  1 22  1 26 28 13  7  6 16 12 27 12  7 12 28 28

TR=mtcars[train,]
TS=mtcars[-train,]
dim(TR)

[1] 25 11

dim(TS)

[1] 16 11

stripchart(TR$mpg~TR$cyl,cex=2)

stripchart(TS$mpg~TS$cyl,col=3,pch=20,cex=2)

X=mtcars[,-mtcars$mpg]
X

                     mpg cyl  disp  hp drat    wt  qsec vs am carb
Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4
Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4
Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    1
Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    1
Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    2
Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    1
Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    4
Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    2
Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    2
Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4
Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4
Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3
Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3
Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3
Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    4
Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    4
Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    4
Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    1
Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    2
Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    1
Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    1
Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    2
AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    2
Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    4
Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    2
Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    1
Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    2
Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    2
Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    4
Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    6
Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    8
Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    2

Y=mtcars$mpg

mo1=lm(mpg~cyl,data=TR)

summary(mo1)


Call:
lm(formula = mpg ~ cyl, data = TR)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.9931 -1.4853  0.3147  1.4226  4.0069 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  37.8088     2.2535  16.778 2.14e-14 ***
cyl          -2.8539     0.3448  -8.278 2.38e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.873 on 23 degrees of freedom
Multiple R-squared:  0.7487,    Adjusted R-squared:  0.7378 
F-statistic: 68.52 on 1 and 23 DF,  p-value: 2.377e-08

SSEMO=sum((mo1$fitted.values-TR$mpg)^2)

length(TR$mpg)

[1] 25

MSEMO=SSEMO/25
MSEMO

[1] 7.594101

sum(mo1$residuals^2)/22

[1] 8.629661

3.367^2

[1] 11.33669

##ee RSE of mo1 is not an MSE (MSE is a biased estimator)


##TEST
motest=lm(mpg~cyl,data=TS)

summary(motest)


Call:
lm(formula = mpg ~ cyl, data = TS)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.8427 -1.9309  0.1055  1.4809  6.2573 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  40.5409     3.0765  13.177 2.79e-09 ***
cyl          -3.2245     0.4719  -6.833 8.16e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.5 on 14 degrees of freedom
Multiple R-squared:  0.7693,    Adjusted R-squared:  0.7528 
F-statistic: 46.69 on 1 and 14 DF,  p-value: 8.155e-06

SSEMOtest=sum((motest$fitted.values-TS$mpg)^2)

length(TS$mpg)

[1] 16

MSEMOt=SSEMOtest/13
MSEMOt

[1] 13.1911

sum(motest$residuals^2)/10

[1] 17.14844

3.191^2

[1] 10.18248

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[1] 4

ABBREVIATIONS

RSE Residuals standard error (lm fx) SSRES/n-p

SSR Sum of squared residuals values