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Multiple Regression and Binomial Regression Sample

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Error(s), warning(s):
The following object is masked from package:ggplot2:

    mpg

Loading required package: zoo

Attaching package: ‘zoo’

The following objects are masked from ‘package:base’:

    as.Date, as.Date.numeric

The following objects are masked from mtcars (pos = 7):

    am, carb, cyl, disp, drat, gear, hp, mpg, qsec, vs, wt

The following object is masked from package:ggplot2:

    mpg


'data.frame':	150 obs. of  5 variables:
 $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
 $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
 $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
 $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
 $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...
  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

Call:
lm(formula = Petal.Length ~ Sepal.Length)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.47747 -0.59072 -0.00668  0.60484  2.49512 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -7.10144    0.50666  -14.02   <2e-16 ***
Sepal.Length  1.85843    0.08586   21.65   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8678 on 148 degrees of freedom
Multiple R-squared:   0.76,	Adjusted R-squared:  0.7583 
F-statistic: 468.6 on 1 and 148 DF,  p-value: < 2.2e-16


Call:
lm(formula = Petal.Length ~ ., data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.78396 -0.15708  0.00193  0.14730  0.65418 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)       -1.11099    0.26987  -4.117 6.45e-05 ***
Sepal.Length       0.60801    0.05024  12.101  < 2e-16 ***
Sepal.Width       -0.18052    0.08036  -2.246   0.0262 *  
Petal.Width        0.60222    0.12144   4.959 1.97e-06 ***
Speciesversicolor  1.46337    0.17345   8.437 3.14e-14 ***
Speciesvirginica   1.97422    0.24480   8.065 2.60e-13 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2627 on 144 degrees of freedom
Multiple R-squared:  0.9786,	Adjusted R-squared:  0.9778 
F-statistic:  1317 on 5 and 144 DF,  p-value: < 2.2e-16


Call:
lm(formula = Petal.Length ~ . - Species, data = iris)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.99333 -0.17656 -0.01004  0.18558  1.06909 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.26271    0.29741  -0.883    0.379    
Sepal.Length  0.72914    0.05832  12.502   <2e-16 ***
Sepal.Width  -0.64601    0.06850  -9.431   <2e-16 ***
Petal.Width   1.44679    0.06761  21.399   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.319 on 146 degrees of freedom
Multiple R-squared:  0.968,	Adjusted R-squared:  0.9674 
F-statistic:  1473 on 3 and 146 DF,  p-value: < 2.2e-16

'data.frame':	32 obs. of  11 variables:
 $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
 $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
 $ disp: num  160 160 108 258 360 ...
 $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
 $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
 $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
 $ qsec: num  16.5 17 18.6 19.4 17 ...
 $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
 $ am  : num  1 1 1 0 0 0 0 0 0 0 ...
 $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
 $ carb: num  4 4 1 1 2 1 4 2 2 4 ...

Call:
glm(formula = am ~ wt, family = binomial(link = "logit"))

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.11400  -0.53738  -0.08811   0.26055   2.19931  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)   
(Intercept)   12.040      4.510   2.670  0.00759 **
wt            -4.024      1.436  -2.801  0.00509 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 43.230  on 31  degrees of freedom
Residual deviance: 19.176  on 30  degrees of freedom
AIC: 23.176

Number of Fisher Scoring iterations: 6

        1 
0.6842243 
'data.frame':	32 obs. of  11 variables:
 $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
 $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
 $ disp: num  160 160 108 258 360 ...
 $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
 $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
 $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
 $ qsec: num  16.5 17 18.6 19.4 17 ...
 $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
 $ am  : num  1 1 1 0 0 0 0 0 0 0 ...
 $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
 $ carb: num  4 4 1 1 2 1 4 2 2 4 ...
 [1] "mpg"  "cyl"  "disp" "hp"   "drat" "wt"   "qsec" "vs"   "am"   "gear"
[11] "carb"
                   mpg cyl disp  hp drat    wt  qsec vs am gear carb
Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

	Shapiro-Wilk normality test

data:  Mod$residuals
W = 0.9373, p-value = 0.0628

Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 2.592692    Df = 1     p = 0.1073577 

	Durbin-Watson test

data:  Mod
DW = 1.636, p-value = 0.09084
alternative hypothesis: true autocorrelation is greater than 0