Is the assumption of conditional independence fulfilled (based on 2D scatterplot)?
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How do I find out based on a scatterplot, if the assumption of conditional independence is fulfilled? I'd be glad about example plots for the following cases:
Case 1: categorical Y, two numerical predictors: conditional independence fulfilled
Case 2: categorical Y, two numerical predictors: conditional independence NOT fulfilled
Below, I provide plots that (I think would fit these 2 cases) but I would like to confirm:
Case 1: scatterplot
For each class, the points seem like a "cloud" of points with almost no trend and no correlation. Hence, given the class Y the two predictor variables (almost) seem independent. Consequently, the assumption of conditional independence seems fulfilled.
Case 2: scatterplot
Consider Y = "setosa" (red points) only. There seems to be a positive linear relationship between the two predictor variables, i.e. they are correlated and not independent. Consequently, the assumption of conditional independence seems NOT fulfilled (although one might argue that it is fulfilled for the other class "virginica").
Is my understanding correct? If not, I'd be glad about an explanation and example plots that do represent the above mentioned cases.
To reproduce the plots in R:
library(ggplot2)
df = iris[-which(iris$Species == "versicolor"), ]
ggplot(df, aes(x = Petal.Width, y = Petal.Length, color = Species)) + geom_point()
ggplot(df, aes(x = Sepal.Width, y = Sepal.Length, color = Species)) + geom_point()
independence conditional-probability
asked Dec 28 '18 at 13:09
jollyplatypusjollyplatypus
11
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add a comment |
$begingroup$
How do I find out based on a scatterplot, if the assumption of conditional independence is fulfilled? I'd be glad about example plots for the following cases:
Case 1: categorical Y, two numerical predictors: conditional independence fulfilled
Case 2: categorical Y, two numerical predictors: conditional independence NOT fulfilled
Below, I provide plots that (I think would fit these 2 cases) but I would like to confirm:
Case 1: scatterplot
For each class, the points seem like a "cloud" of points with almost no trend and no correlation. Hence, given the class Y the two predictor variables (almost) seem independent. Consequently, the assumption of conditional independence seems fulfilled.
Case 2: scatterplot
Consider Y = "setosa" (red points) only. There seems to be a positive linear relationship between the two predictor variables, i.e. they are correlated and not independent. Consequently, the assumption of conditional independence seems NOT fulfilled (although one might argue that it is fulfilled for the other class "virginica").
Is my understanding correct? If not, I'd be glad about an explanation and example plots that do represent the above mentioned cases.
To reproduce the plots in R:
library(ggplot2)
df = iris[-which(iris$Species == "versicolor"), ]
ggplot(df, aes(x = Petal.Width, y = Petal.Length, color = Species)) + geom_point()
ggplot(df, aes(x = Sepal.Width, y = Sepal.Length, color = Species)) + geom_point()
independence conditional-probability
asked Dec 28 '18 at 13:09
jollyplatypusjollyplatypus
11
$endgroup$
add a comment |
$begingroup$
How do I find out based on a scatterplot, if the assumption of conditional independence is fulfilled? I'd be glad about example plots for the following cases:
Case 1: categorical Y, two numerical predictors: conditional independence fulfilled
Case 2: categorical Y, two numerical predictors: conditional independence NOT fulfilled
Below, I provide plots that (I think would fit these 2 cases) but I would like to confirm:
Case 1: scatterplot
For each class, the points seem like a "cloud" of points with almost no trend and no correlation. Hence, given the class Y the two predictor variables (almost) seem independent. Consequently, the assumption of conditional independence seems fulfilled.
Case 2: scatterplot
Consider Y = "setosa" (red points) only. There seems to be a positive linear relationship between the two predictor variables, i.e. they are correlated and not independent. Consequently, the assumption of conditional independence seems NOT fulfilled (although one might argue that it is fulfilled for the other class "virginica").
Is my understanding correct? If not, I'd be glad about an explanation and example plots that do represent the above mentioned cases.
To reproduce the plots in R:
library(ggplot2)
df = iris[-which(iris$Species == "versicolor"), ]
ggplot(df, aes(x = Petal.Width, y = Petal.Length, color = Species)) + geom_point()
ggplot(df, aes(x = Sepal.Width, y = Sepal.Length, color = Species)) + geom_point()
independence conditional-probability
asked Dec 28 '18 at 13:09
jollyplatypusjollyplatypus
11
$endgroup$
How do I find out based on a scatterplot, if the assumption of conditional independence is fulfilled? I'd be glad about example plots for the following cases:
Case 1: categorical Y, two numerical predictors: conditional independence fulfilled
Case 2: categorical Y, two numerical predictors: conditional independence NOT fulfilled
Below, I provide plots that (I think would fit these 2 cases) but I would like to confirm:
Case 1: scatterplot
For each class, the points seem like a "cloud" of points with almost no trend and no correlation. Hence, given the class Y the two predictor variables (almost) seem independent. Consequently, the assumption of conditional independence seems fulfilled.
Case 2: scatterplot
Consider Y = "setosa" (red points) only. There seems to be a positive linear relationship between the two predictor variables, i.e. they are correlated and not independent. Consequently, the assumption of conditional independence seems NOT fulfilled (although one might argue that it is fulfilled for the other class "virginica").
Is my understanding correct? If not, I'd be glad about an explanation and example plots that do represent the above mentioned cases.
To reproduce the plots in R:
library(ggplot2)
df = iris[-which(iris$Species == "versicolor"), ]
ggplot(df, aes(x = Petal.Width, y = Petal.Length, color = Species)) + geom_point()
ggplot(df, aes(x = Sepal.Width, y = Sepal.Length, color = Species)) + geom_point()
independence conditional-probability
independence conditional-probability
asked Dec 28 '18 at 13:09
jollyplatypusjollyplatypus
11
asked Dec 28 '18 at 13:09
jollyplatypusjollyplatypus
11
asked Dec 28 '18 at 13:09
jollyplatypusjollyplatypus
11
asked Dec 28 '18 at 13:09
jollyplatypusjollyplatypus
11
asked Dec 28 '18 at 13:09
jollyplatypusjollyplatypus
11
11
add a comment |
add a comment |
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