r:dummy_variables_with_significant_interaction
Table of Contents
Regression with two categorical variables (IVs): Two way anova
college <- read.csv("http://commres.net/wiki/_media/r/college.csv")
attach(college)
str(college)
head(college)
salary <- salary / 1000
public<-factor(public, c(0,1), labels=c('Private', 'Public'))
location<-factor(location, c(1,2,3,4), labels=c('S', 'MW','NE', 'W'))
m1 <- lm(salary~public+location)
m2 <- lm(salary~public*location)
summary(m1)
summary(m2)
a.m2 <- aov(salary~public*location)
summary(a.m2)
interaction.plot(x.factor = location,
trace.factor = public,
response = salary,
fun = median,
ylab = "salary",
xlab = "location",
col=c("red", "blue"),
lty = 1,
lwd=2,
trace.label="public")
output
####################
> college <- read.csv("http://commres.net/wiki/_media/r/college.csv")
> attach(college)
The following object is masked from acne.re (pos = 36):
id
The following object is masked from acne.re (pos = 37):
id
> str(college)
'data.frame': 85 obs. of 6 variables:
$ id : int 1 2 3 4 5 6 7 8 9 10 ...
$ name : chr "Massachusetts Institute of Technology (MIT)" "Harvard University" "Dartmouth College" "Princeton University" ...
$ salary : num 119000 121000 123000 123000 110000 112000 111000 117000 111000 104000 ...
$ cost : int 189300 189600 188400 188700 194200 181900 191300 187600 180400 184900 ...
$ public : int 0 0 0 0 0 0 0 0 0 0 ...
$ location: int 3 3 3 3 3 2 3 1 3 3 ...
> head(college)
id name salary cost public location
1 1 Massachusetts Institute of Technology (MIT) 119000 189300 0 3
2 2 Harvard University 121000 189600 0 3
3 3 Dartmouth College 123000 188400 0 3
4 4 Princeton University 123000 188700 0 3
5 5 Yale University 110000 194200 0 3
6 6 University of Notre Dame 112000 181900 0 2
> salary <- salary / 1000
> public<-factor(public, c(0,1), labels=c('Private', 'Public'))
> location<-factor(location, c(1,2,3,4), labels=c('S', 'MW','NE', 'W'))
> m1 <- lm(salary~public+location)
> m2 <- lm(salary~public*location)
> summary(m1)
Call:
lm(formula = salary ~ public + location)
Residuals:
Min 1Q Median 3Q Max
-17.15 -4.75 -0.35 2.85 31.67
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 99.56 1.90 52.30 < 2e-16 ***
publicPublic -7.30 1.83 -3.99 0.00014 ***
locationMW -2.40 2.52 -0.95 0.34366
locationNE 8.79 2.39 3.68 0.00042 ***
locationW -10.93 2.49 -4.39 3.4e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 7.86 on 80 degrees of freedom
Multiple R-squared: 0.587, Adjusted R-squared: 0.566
F-statistic: 28.4 on 4 and 80 DF, p-value: 1.06e-14
> summary(m2)
Call:
lm(formula = salary ~ public * location)
Residuals:
Min 1Q Median 3Q Max
-11.19 -4.88 -0.65 2.49 27.55
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 99.492 2.006 49.60 < 2e-16 ***
publicPublic -7.142 3.172 -2.25 0.0272 *
locationMW -1.982 2.975 -0.67 0.5074
locationNE 11.393 2.537 4.49 2.5e-05 ***
locationW -17.554 3.172 -5.53 4.1e-07 ***
publicPublic:locationMW -0.913 4.500 -0.20 0.8398
publicPublic:locationNE -12.843 4.704 -2.73 0.0078 **
publicPublic:locationW 10.650 4.451 2.39 0.0192 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 6.95 on 77 degrees of freedom
Multiple R-squared: 0.689, Adjusted R-squared: 0.661
F-statistic: 24.4 on 7 and 77 DF, p-value: <2e-16
>
>
> a.m2 <- aov(salary~public*location)
> summary(a.m2)
Df Sum Sq Mean Sq F value Pr(>F)
public 1 2970 2970 61.50 2.0e-11 ***
location 3 4057 1352 28.01 2.4e-12 ***
public:location 3 1225 408 8.46 6.3e-05 ***
Residuals 77 3718 48
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
>
> interaction.plot(x.factor = location,
+ trace.factor = public,
+ response = salary,
+ fun = median,
+ ylab = "salary",
+ xlab = "location",
+ col=c("red", "blue"),
+ lty = 1,
+ lwd=2,
+ trace.label="public")
>
Regression with a continous + a categorical variables: ANCOVA
summary(mod<-lm(salary~cost + location)) anova(mod)
> summary(mod<-lm(salary~cost + location))
Call:
lm(formula = salary ~ cost + location)
Residuals:
Min 1Q Median 3Q Max
-20.244 -4.933 -0.572 3.162 29.939
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.78e+01 3.10e+00 28.34 < 2e-16 ***
cost 6.05e-05 1.73e-05 3.50 0.00076 ***
locationMW -2.80e+00 2.57e+00 -1.09 0.27885
locationNE 9.23e+00 2.42e+00 3.81 0.00027 ***
locationW -1.05e+01 2.57e+00 -4.10 0.00010 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 8.02 on 80 degrees of freedom
Multiple R-squared: 0.571, Adjusted R-squared: 0.549
F-statistic: 26.6 on 4 and 80 DF, p-value: 4.96e-14
> anova(mod)
Analysis of Variance Table
Response: salary
Df Sum Sq Mean Sq F value Pr(>F)
cost 1 2757 2757 42.9 5.1e-09 ***
location 3 4072 1357 21.1 3.6e-10 ***
Residuals 80 5141 64
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
(Intercept) 8.78e+01 3.10e+00 28.34 < 2e-16 *** cost 6.05e-05 1.73e-05 3.50 0.00076 *** locationMW -2.80e+00 2.57e+00 -1.09 0.27885 locationNE 9.23e+00 2.42e+00 3.81 0.00027 *** locationW -1.05e+01 2.57e+00 -4.10 0.00010 ***
y hat ~ 87.8 + .00006*cost - 2.8 MW + 9.23 NE - 10.5 E
- S, MW, NE, W 중에서 S가 default
- y hat ~ 87.8 + .00006*cost
- MW:
- y hat ~ 87.8 - 2.8 + .00006*cost
- y hat ~ 85 + .00006*cost
- NE:
- y hat ~ 87.8 - 9.23 + .00006*cost
- y hat ~ 78.57 + .00006*cost
- E:
- y hat ~ 87.8 - 10.5 + .00006*cost
- y hat ~ 77.3 + .00006*cost
> summary(mod2<-lm(salary~cost * location))
Call:
lm(formula = salary ~ cost * location)
Residuals:
Min 1Q Median 3Q Max
-17.1126 -5.6241 -0.8152 2.6401 28.4861
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.863e+01 4.995e+00 17.744 <2e-16 ***
cost 5.480e-05 3.211e-05 1.707 0.0919 .
locationMW -5.526e+00 7.213e+00 -0.766 0.4460
locationNE -2.866e+00 7.383e+00 -0.388 0.6989
locationW -1.876e+00 6.509e+00 -0.288 0.7740
cost:locationMW 1.885e-05 4.681e-05 0.403 0.6882
cost:locationNE 7.480e-05 4.533e-05 1.650 0.1030
cost:locationW -7.815e-05 4.665e-05 -1.675 0.0980 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 7.644 on 77 degrees of freedom
Multiple R-squared: 0.6241, Adjusted R-squared: 0.5899
F-statistic: 18.26 on 7 and 77 DF, p-value: 4.313e-14
> anova(mod2)
Analysis of Variance Table
Response: salary
Df Sum Sq Mean Sq F value Pr(>F)
cost 1 2757.0 2756.97 47.183 1.470e-09 ***
location 3 4071.8 1357.26 23.228 8.276e-11 ***
cost:location 3 641.6 213.86 3.660 0.01596 *
Residuals 77 4499.2 58.43
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
r/dummy_variables_with_significant_interaction.txt · Last modified: 2023/06/05 22:01 by hkimscil