add statistical analysis section with general linear models

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Kristin Linn 2015-10-20 16:22:40 -04:00
parent 4a3d521430
commit 11aab085d6

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@ -3,6 +3,7 @@ language: R
contributors:
- ["e99n09", "http://github.com/e99n09"]
- ["isomorphismes", "http://twitter.com/isomorphisms"]
- ["kalinn", "http://github.com/kalinn"]
filename: learnr.r
---
@ -196,6 +197,14 @@ class(NaN) # "numeric"
# You can do arithmetic on two vectors with length greater than 1,
# so long as the larger vector's length is an integer multiple of the smaller
c(1,2,3) + c(1,2,3) # 2 4 6
# Since a single number is a vector of length one, scalars are applied
# elementwise to vectors
(4 * c(1,2,3) - 2) / 2 # 1 3 5
# Except for scalars, use caution when performing arithmetic on vectors with
# different lengths. Although it can be done,
c(1,2,3,1,2,3) * c(1,2) # 1 4 3 2 2 6
# Matching lengths is better practice and easier to read
c(1,2,3,1,2,3) * c(1,2,1,2,1,2)
# CHARACTERS
# There's no difference between strings and characters in R
@ -234,6 +243,9 @@ class(NA) # "logical"
TRUE | FALSE # TRUE
# AND
TRUE & FALSE # FALSE
# Applying | and & to vectors returns elementwise logic operations
c(TRUE,FALSE,FALSE) | c(FALSE,TRUE,FALSE) # TRUE TRUE FALSE
c(TRUE,FALSE,TRUE) & c(FALSE,TRUE,TRUE) # FALSE FALSE TRUE
# You can test if x is TRUE
isTRUE(TRUE) # TRUE
# Here we get a logical vector with many elements:
@ -663,6 +675,95 @@ write.csv(pets, "pets2.csv") # to make a new .csv file
#########################
# Statistical Analysis
#########################
# Linear regression!
linearModel <- lm(price ~ time, data = list1)
linearModel # outputs result of regression
# =>
# Call:
# lm(formula = price ~ time, data = list1)
#
# Coefficients:
# (Intercept) time
# 0.1453 0.4943
summary(linearModel) # more verbose output from the regression
# =>
# Call:
# lm(formula = price ~ time, data = list1)
#
# Residuals:
# Min 1Q Median 3Q Max
# -8.3134 -3.0131 -0.3606 2.8016 10.3992
#
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 0.14527 1.50084 0.097 0.923
# time 0.49435 0.06379 7.749 2.44e-09 ***
# ---
# Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
#
# Residual standard error: 4.657 on 38 degrees of freedom
# Multiple R-squared: 0.6124, Adjusted R-squared: 0.6022
# F-statistic: 60.05 on 1 and 38 DF, p-value: 2.44e-09
coef(linearModel) # extract estimated parameters
# =>
# (Intercept) time
# 0.1452662 0.4943490
summary(linearModel)$coefficients # another way to extract results
# =>
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 0.1452662 1.50084246 0.09678975 9.234021e-01
# time 0.4943490 0.06379348 7.74920901 2.440008e-09
summary(linearModel)$coefficients[,4] # the p-values
# =>
# (Intercept) time
# 9.234021e-01 2.440008e-09
# GENERAL LINEAR MODELS
# Logistic regression
set.seed(1)
list1$success = rbinom(length(list1$time), 1, .5) # random binary
glModel <- glm(success ~ time, data = list1,
family=binomial(link="logit"))
glModel # outputs result of logistic regression
# =>
# Call: glm(formula = success ~ time,
# family = binomial(link = "logit"), data = list1)
#
# Coefficients:
# (Intercept) time
# 0.17018 -0.01321
#
# Degrees of Freedom: 39 Total (i.e. Null); 38 Residual
# Null Deviance: 55.35
# Residual Deviance: 55.12 AIC: 59.12
summary(glModel) # more verbose output from the regression
# =>
# Call:
# glm(formula = success ~ time,
# family = binomial(link = "logit"), data = list1)
# Deviance Residuals:
# Min 1Q Median 3Q Max
# -1.245 -1.118 -1.035 1.202 1.327
#
# Coefficients:
# Estimate Std. Error z value Pr(>|z|)
# (Intercept) 0.17018 0.64621 0.263 0.792
# time -0.01321 0.02757 -0.479 0.632
#
# (Dispersion parameter for binomial family taken to be 1)
#
# Null deviance: 55.352 on 39 degrees of freedom
# Residual deviance: 55.121 on 38 degrees of freedom
# AIC: 59.121
#
# Number of Fisher Scoring iterations: 3
#########################
# Plots
#########################
@ -670,9 +771,6 @@ write.csv(pets, "pets2.csv") # to make a new .csv file
# BUILT-IN PLOTTING FUNCTIONS
# Scatterplots!
plot(list1$time, list1$price, main = "fake data")
# Regressions!
linearModel <- lm(price ~ time, data = list1)
linearModel # outputs result of regression
# Plot regression line on existing plot
abline(linearModel, col = "red")
# Get a variety of nice diagnostics
@ -696,7 +794,6 @@ pp + geom_point()
# ggplot2 has excellent documentation (available http://docs.ggplot2.org/current/)
```
## How do I get R?