Multiple Regression and Binomial Regression Sample
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
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