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zhttps://github.com/lmu-osc/Introduction-Simulations-in-R-exercices ([here](https://lmu-osc.github.io/Collaborative-RStudio-GitHub/) is a reminder on how to do this). -## B. You do not know version control, and/or simply want to download a copy of this material +### B. You do not know version control -**1) Download the repository** -Please download the GitHub repository that we are using today: https://github.com/lmu-osc/Introduction-Simulations-in-R. +Download the exercises repository associated with this tutorial: https://github.com/lmu-osc/Introduction-Simulations-in-R-exercices.
@@ -19,21 +20,13 @@ Please download the GitHub repository that we are using today: -
- -Select the downloaded (and extracted) folder by clicking on 'Browse', then select 'Create Project'. -
- -
+Find the downloaded (and extracted) folder and double click on the .Rproj file. -In the panel containing the 'Files' tab, find the exercise sheet and open it by double clicking on it. +In the panel containing the 'Files' tab, find the exercise sheet of your choice (with or without solutions) and open it by clicking on it.

From 0c9a4bb3b3c13219e107763a972821d302c70c44 Mon Sep 17 00:00:00 2001 From: Malika Ihle <16382829+MalikaIhle@users.noreply.github.com> Date: Thu, 24 Sep 2026 11:53:47 +0200 Subject: [PATCH 3/4] delete exercises script now in separate exercise repo --- exercise-script-with-solutions.R | 549 ---------------------------- exercise-script-without-solutions.R | 252 ------------- 2 files changed, 801 deletions(-) delete mode 100644 exercise-script-with-solutions.R delete mode 100644 exercise-script-without-solutions.R diff --git a/exercise-script-with-solutions.R b/exercise-script-with-solutions.R deleted file mode 100644 index 2f61ad0..0000000 --- a/exercise-script-with-solutions.R +++ /dev/null @@ -1,549 +0,0 @@ -############################################################################################################### -# This R script contains # -# - the examples shown in the step-by-step workshop pages # -# (for you to run line-by-line to observe the outcome, or to modify and play with) # -# - space called 'YOUR TURN' for you to write your own code to answer the exercises from the workshop pages # -# - a possible solution to those exercises # -############################################################################################################### - -#~~~~~~~~~ Random Numbers Generators and sampling theory ----- - -# sample - -## x is a sequence -x <- 1:10 -x -?sample # default: replace = FALSE -sample(x) -sample(x, replace = TRUE) -sample(letters, size = 10) -sample(x, size = 100, replace = TRUE) - -## x is a vector of combined values -x <- c(1,5,8) -x -sample(x, size = 6, replace = TRUE) - - - - -# YOUR TURN: generate random numbers -## Sample 100 values between 3 and 103 with replacement - - - - - - - -### possible solutions ### -x <- 3:103 -sample(x, 100, replace = TRUE) -########################## - - -# random number generator drawing from specific distributions -?runif # runif(n, min, max) -?rpois # rpois(n, lambda) -?rnorm # rnorm(n, mean, sd) -?rbinom # rbinom(n, prob) - - - -# YOUR TURN: generate random numbers -## Draw 100 values from a normal distribution with a mean of 0 and a sd of 1 - - - - - - - - - -### possible solutions ### -rnorm(n = 100, mean = 0, sd = 1) -rnorm(100) # if you sample from a normal distribution with a mean of 0 and a sd of 1, you do not need to provide them, they are the defaults -rnorm(100,0,1) # you do not need to label the arguments if you provide them in their default order, but you should provide names if they overwrite default values -########################## - -## Draw 50 values from a normal distribution with a mean of 10 and sd of 5 - - - - - - - - - -### possible solutions ### -rnorm(sd = 5, mean = 10, n = 50) # if you label your arguments you can put them in whatever order you want! -rnrom(50, mean = 10, sd = 5) # using the rules above: non-default arguments in order, followed by named arguments using names -########################## - -## Draw 1000 values from a poisson distribution with a lambda of 50 - - - - - - - - - -### possible solutions ### -rpois(n = 1000, lambda = 50) -rpois(1000,50) -########################## - -## Draw 30 values from a uniform distribution between 0 and 10 - - - - - - - - -### possible solutions ### -runif(n = 30, min = 0, max = 10) -runif(30, max = 10) # we can omit min = 0 because that's the default -########################## - - - -# repeat -?replicate # replicate(n, expression) -rnorm(10) -mean(rnorm(10)) -replicate(10,rnorm(10)) -replicate(10, mean(rnorm(100))) -hist(replicate(10, mean(rnorm(100)))) - -# YOUR TURN: generate random numbers, repeat, and plot -## Replicate 1000 times the mean of 10 values drawn from a uniform distribution between 0 and 10 - - - - - - - - - -### possible solutions ### -replicate(1000, mean(runif(10, max = 10))) -hist(replicate(1000, mean(runif(10, max = 10)))) -########################## - -## Replicate 100 times the mean of 50 values drawn from a normal distribution of mean 10 and standard deviation 5 - - - - - - - - - - -### possible solutions ### -replicate(100, mean(rnorm(50, mean = 10, sd = 5))) -hist(replicate(100, mean(rnorm(50, mean = 10, sd = 5)))) -########################## - - -# set seed -hist(replicate(100, mean(rnorm(10)))) -hist(replicate(100, mean(rnorm(10)))) -hist(replicate(100, mean(rnorm(10)))) - -set.seed(10) -hist(replicate(100, mean(rnorm(10)))) - -set.seed(10) -hist(replicate(100, mean(rnorm(10)))) - - -# defining sample size within a replication (n) and the number of simulation/repeats/replication (nrep) -## single random sample of normal distribution N(0,1) with n = 10 -set.seed(10) -x <- rnorm(10) # mean = 0, sd = 1 are the defaults -hist(x, breaks = 10, col = "grey", xlim = c(-4,4)) -abline(v = 0, col = "red", lty = 2, lwd = 2) -abline(v = mean(x), col = "blue", lwd = 2) -par(xpd = TRUE) # turn off clipping of legend -# where a function has a long list of arguments, we can put them on a new line each -legend( - 0.9, - y = 1.5, - legend = c("mean(x)", "0"), - lty = c(1, 2), - col = c("blue","red") -) - -## 24 sims of same distribution N(0,1) with n = 10 -set.seed(10) -x24 <- replicate(24, rnorm(10)) -par(mfrow = c(3,8), mar = c(0,0,0,0)) -# apply is complicated because it takes a function as one of its arguments -x24Plot <- apply( - x24, - 2, - function(x) { - # for fairly simple functions with lots of arguments, we sometimes just cram them all on the same line. - # it's not great practice but it stops the script getting super long when dealing with graphical objects - hist(x, col = "grey", xlim = c(-5,5), ylim = c(0,7), breaks = c(-5:5), - main = "", ylab = "", xlab = "", xaxt = "n", yaxt = "n") - abline(v = mean(x), col = "blue", lwd = 2) - abline(v = 0, col = "red", lty = 2, lwd = 2) - } -) - -## distribution of means and sd from 24 sims N(0,1) with n = 10 -par(mfrow = c(1,2), mar = c(5,5,1,1)) -hist(apply(x24, 2, mean), main = "Mean", col = "grey", xlim = c(-1,1)) -abline(v = 0, col = "red", lty = 2, lwd = 2) -hist(apply(x24, 2, sd), main = "SD",col = "grey", xlim = c(0.6,1.4)) -abline(v = 1, col = "red", lty = 2, lwd = 2) - -## 24 sims of same distribution N(0,1) with n = 1000 -set.seed(10) -x24b <- replicate(24, rnorm(1000)) -par(mfrow = c(3,8), mar = c(0,0,0,0)) -x24bPlot <- apply( - x24b, - 2, - function(x){ - hist(x, col = "grey", xlim = c(-5,5), ylim = c(0,500), breaks = c(-5:5), - main = "", ylab = "", xlab = "", xaxt = "n", yaxt = "n") - abline(v = mean(x), col = "blue", lwd = 2) - abline(v = 0, col = "red", lty = 2, lwd = 2) - } -) - -## distribution of means and SDs from 24 sims N(0,1) with n = 1000 -par(mfrow = c(1,2), mar = c(5,5,1,1)) -hist(apply(x24b, 2, mean), main = "Mean",col = "grey", xlim = c(-1,1)) -abline(v = 0, col = "red", lty = 2, lwd = 2) -hist(apply(x24b, 2, sd), main = "SD",col = "grey", xlim = c(0.6,1.4)) -abline(v = 1, col = "red", lty = 2, lwd = 2) - -## distribution of means and SDs from 1000 sims N(0,1) with n = 10 -set.seed(10) -x1000 <- replicate(1000, rnorm(10)) -par(mfrow = c(1,2), mar = c(5,5,1,1)) -hist(apply(x1000, 2, mean), main = "Mean",col = "grey") -abline(v = 0, col = "red", lty = 2, lwd = 2) -hist(apply(x1000, 2, sd), main = "SD",col = "grey") -abline(v = 1, col = "red", lty = 2, lwd = 2) - - -#~~~~~~~~~ Functions ----- - -# writing a function -## function syntax: -## AwesomeFunctionName <- function(argument1, argument2,…){ -## do stuff here -## } -## The last thing that appears in the 'do stuff here' section is the function's -## "return value" - -# YOUR TURN: write a function that takes input "nrep", replicates '(mean(rnorm(100)))' -# nrep times, and draws a histogram of the results - - - - - - - - - - - - -### possible solutions ### -#### step 1: the action -mean(rnorm(100)) -#### step 2: replicate the action 1000 times -replicate(1000, mean(rnorm(100))) -#### step 3: plot the outcome of those simulations -hist(replicate(1000, mean(rnorm(100)))) -#### step 4: replicate the action nrep time, with nrep defined outside the function -nrep <- 1000 -replicate(nrep, mean(rnorm(100))) -#### step 5: wrap it in a function: -histrnorm100 <- function(nrep){ - hist(replicate(nrep, mean(rnorm(100)))) -} -#### step 6: check that the function works -histrnorm100(9) -histrnorm100(1000) -########################## - -# YOUR TURN: modify your function -## to draw a histogram of nrep mean(rnorm(n)), where n is another input - - - - - - - - - - - - - - - - -### possible solutions ### -#### step 4: define parameters outside the function -nrep <- 100 -n <- 10 -replicate(nrep, mean(rnorm(n))) -#### step 5: wrap the action in a function: -histrnorm_n <- function(nrep, n){ - hist(replicate(nrep, mean(rnorm(n)))) -} -#### step 6: check that the function works -histrnorm_n(10,10) -histrnorm_n(10,100) -histrnorm_n(100,100) -histrnorm_n(1000,100) -########################## - - -#~~~~~~~~~ Simulating no effect and check alpha ----- - -# YOUR TURN: draw from the same normal distribution twice -## and see if the sample differ from each other -## will they differ significantly in 5% of the nrep? -### Figure out how to do a t.test in R -### Generate two vectors of 10 values drawn from N(0,1) and compare them with a t test -### Figure out how to extract the p-value from that object (HINT use `str` or `names`) -### Write a function simT that generates two vectors of n random normals, compare them with a t test and return the p-value -### Repeat with nrep = 20 and draw a histogram for n = 10 -### Repeat with nrep = 100 and draw a histogram for n = 10 - - - - - - - - - - - - - - - - -### possible solutions ### -#### Figure out how to do a t.test in R -?t.test -#### Generate two vectors of 10 N(0,1) -x1 <- rnorm(10,0,1) -x2 <- rnorm(10,0,1) -#### Compare them with a t test -t.test(x1,x2) -#### extract p value -str(t.test(x1,x2)) -t.test(x1,x2)$p.value -#### write function -simT <- function(n){ - x1 <- rnorm(n,0,1) - x2 <- rnorm(n,0,1) - t.test(x1, x2)$p.value -} -#### test function -simT(50) - -#### repeat function for n = 10 and for different nrep and plot -par(mfrow = c(1,2)) -simTRep <- replicate(20, simT(10)) -hist(simTRep, breaks = 21, col = c('red',rep('grey',20)), - main = "nrep = 20, n = 10", xlab = "pvalue") - -simTRep2 <- replicate(100, simT(10)) -hist(simTRep2, breaks = 21, col = c('red',rep('grey',20)), - main = "nrep = 100, n = 10", xlab = "pvalue") -########################## - -#### repeat function for nrep = 1000 and various n -par(mfrow = c(1,2)) -simTRep <- replicate(1000, simT(10)) -hist(simTRep, breaks = 21, col = c('red',rep('grey',20)), - main = "nrep = 1000, n = 10", xlab = "pvalue") - -simTRep2 <- replicate(1000, simT(100)) -hist(simTRep2, breaks = 21, col = c('red',rep('grey',20)), - main = "nrep = 1000, n = 100", xlab = "pvalue") - - -#~~~~~~~~~ Simulating an effect and check power ----- - -# we can calculate the power of a t.test for a given sample size using: -power.t.test(n = NULL, delta = 0.5, sd = 1, sig.level = 0.05, power = 0.8) -# the required sample size is 64 per group. - -# YOUR TURN: Use your simulation skills to work out the power of a t-test for a given sample size through simulation. -## Write a function which: -### 1. Draws n values from a random normal distribution with mean 1, and another n values from a normal distribution with mean 2 -### 2. Compares the means of these two samples with a t.test and extracts the p.value -## Then, use that function to replicate the function 1000 times using the parameters used in the power calculation above (that used the power.t.test function). -## Calculate the proportion of p-values that are <0.05 - - - - - - - - - - - -### possible solution ### -#### write new function -simT2 <- function(n, m1, m2) { - ##### n is sample size per group, m1 is mean of group 1, m2 is mean of group 2 - x1 <- rnorm(n, m1) - x2 <- rnorm(n, m2) - t.test(x1, x2)$p.value -} - -##### repeat the function 1000 times -##### note that we are using a difference of 0.5 between means to match the "delta" -##### used in the power calculation -set.seed(100) -p <- replicate(1000, simT2(n = 64, m1 = 0, m2 = 0.5)) - -#### plot the results -par(mfrow = c(1,1)) -hist(p, breaks = 21, col = c('red',rep('grey',20)), - main = "nrep = 1000, n = 64, delta = 0.5", xlab = 'pvalue') - -#### calculate the proportion "significant" -prop.table(table(p < 0.05)) - -########################## - -#### power is the probability that the test correctly rejects the null. Since we -#### know the population paramaters (as we set them in our simulation), we know -#### that there really is a difference, and the null should be rejected. The power -#### is therefore the proportion of p.values <0.05 - -# compare that to calculating the "power" parameter using the function below with all the other parameters provided (including n) -power.t.test(n = 64, delta = 0.5, sd = 1) # the results are similar - - -#~~~~~~~~~ Simulating for a preregistration ----- - -# YOUR TURN: -## Try to make a dataset that looks like this, using the -## functions `data.frame()`, `sample()`, and `rnorm()` - -# smoking_status lung_cancer sex age -# 1 Yes No M 12.67918 -# 2 Yes Yes F 23.71397 -# 3 No No M 28.87786 -# 4 Yes No F 28.99327 -# 5 Yes Yes F 30.41415 -# 6 No No M 44.60615 - - - - - - - - - - - - -#### possible solution ### -set.seed(1234) -N <- 10 # size of your dataset -yes_no <- c("Yes", "No") # some options for the outcomes in the data - -# the dataframe() function let's us create a data frame -# before the " = " is the column name. After " = " is the contents of the columm -df <- data.frame( - smoking_status = sample(yes_no, size = N, replace = T), - lung_cancer = sample(yes_no, size = N, replace = T), - sex = sample(c("M", "F"), size = N, replace = T), - age = rnorm(N, 30, sd = 10) -) -# run the parts after the " = " alone to make sure you understand what's going on -sample(c("M", "F"), size = N, replace = T) - -head(df) -########################## - -# YOUR TURN: -## Run a logistic regression on the data with lung cancer as the outcome and -## adjusting for the other variables. -## You could try something like: -## glm(lung_cancer ~ smoking_status, sex, age, family = binomial(link = "logit"), data = df) -## Why doesn't it work? Try to trouble shoot and get the code to work! - -## HINT: are the variables the correct data type? -## HINT: once the model works, use summary() to look at the results - - - - - - - - - - - -#### possible solution ### - -# This mysterious error message appears because the categorical variables -# need to be factors for the model to run. So we are already learning -# something about how the data need to be that you might not have known -# before trying to run the code on a simulated dataset. - -# You can convert the relevant variables to factors -df[1:3] <- lapply(df[1:3], as.factor) - -# You could also do this one variable at a time: -# df$smoking_status <- as.factor(df$smoking_status) - -# Now we can rerun the model: - -m1 <- glm( - lung_cancer ~ smoking_status + sex + age, - family = binomial(link = "logit"), - data = df -) - -# and look at the results -summary(m1) -########################## - - - - - - - - - - - - - - - diff --git a/exercise-script-without-solutions.R b/exercise-script-without-solutions.R deleted file mode 100644 index 51086fa..0000000 --- a/exercise-script-without-solutions.R +++ /dev/null @@ -1,252 +0,0 @@ -############################################################################################################### -# This R script contains # -# - the examples shown in the step-by-step workshop pages # -# (for you to run line-by-line to observe the outcome, or to modify and play with) # -# - space called 'YOUR TURN' for you to write your own code to answer the exercises from the workshop pages # -############################################################################################################### - -#~~~~~~~~~ Random Numbers Generators and sampling theory ----- - -# sample - -## x is a sequence -x <- 1:10 -x -?sample # default: replace = FALSE -sample(x) -sample(x, replace = TRUE) -sample(letters, size = 10) -sample(x, size = 100, replace = TRUE) - -## x is a vector of combined values -x <- c(1,5,8) -x -sample(x, size = 6, replace = TRUE) - - -# YOUR TURN: generate random numbers -## Sample 100 values between 3 and 103 with replacement - - - -# random number generator drawing from specific distributions - -?runif # runif(n, min, max) -?rpois # rpois(n, lambda) -?rnorm # rnorm(n, mean, sd) -?rbinom # rbinom(n, prob) - -# YOUR TURN: generate random numbers -## Draw 100 values from a normal distribution with a mean of 0 and a sd of 1 - - -## Draw 50 values from a normal distribution with a mean of 10 and sd of 5 - - -## Draw 1000 values from a poisson distribution with a lambda of 50 - - -## Draw 30 values from a uniform distribution between 0 and 10 - - - - -# repeat - -?replicate # replicate(n, expression) -rnorm(10) -mean(rnorm(10)) -replicate(10,rnorm(10)) -replicate(10, mean(rnorm(100))) -hist(replicate(10, mean(rnorm(100)))) - -# YOUR TURN: generate random numbers, repeat, and plot -## Replicate 1000 times the mean of 10 values drawn from a uniform distribution between 0 and 10 - - -## Replicate 100 times the mean of 50 values drawn from a normal distribution of mean 10 and standard deviation 5 - - - - -# set seed - -hist(replicate(100, mean(rnorm(10)))) -hist(replicate(100, mean(rnorm(10)))) -hist(replicate(100, mean(rnorm(10)))) - -set.seed(10) -hist(replicate(100, mean(rnorm(10)))) - -set.seed(10) -hist(replicate(100, mean(rnorm(10)))) - - -# defining sample size within a replication (n) and the number of simulation/repeats/replication (nrep) -## single random sample of normal distribution N(0,1) with n = 10 -set.seed(10) -x <- rnorm(10) # mean = 0, sd = 1 are the defaults -hist(x, breaks = 10, col = "grey", xlim = c(-4,4)) -abline(v = 0, col = "red", lty = 2, lwd = 2) -abline(v = mean(x), col = "blue", lwd = 2) -par(xpd = TRUE) # turn off clipping of legend -# where a function has a long list of arguments, we can put them on a new line each -legend( - 0.9, - y = 1.5, - legend = c("mean(x)", "0"), - lty = c(1, 2), - col = c("blue","red") -) - -## 24 sims of same distribution N(0,1) with n = 10 -set.seed(10) -x24 <- replicate(24, rnorm(10)) -par(mfrow = c(3,8), mar = c(0,0,0,0)) -# apply is complicated because it takes a function as one of its arguments -x24Plot <- apply( - x24, - 2, - function(x) { - # for fairly simple functions with lots of arguments, we sometimes just cram them all on the same line. - # it's not great practice but it stops the script getting super long when dealing with graphical objects - hist(x, col = "grey", xlim = c(-5,5), ylim = c(0,7), breaks = c(-5:5), - main = "", ylab = "", xlab = "", xaxt = "n", yaxt = "n") - abline(v = mean(x), col = "blue", lwd = 2) - abline(v = 0, col = "red", lty = 2, lwd = 2) - } -) - -## distribution of means and SDs from 24 sims N(0,1) with n = 10 -par(mfrow = c(1,2), mar = c(5,5,1,1)) -hist(apply(x24, 2, mean), main = "Mean", col = "grey", xlim = c(-1,1)) -abline(v = 0, col = "red", lty = 2, lwd = 2) -hist(apply(x24, 2, sd), main = "SD",col = "grey", xlim = c(0.6,1.4)) -abline(v = 1, col = "red", lty = 2, lwd = 2) - -## 24 sims of same distribution N(0,1) with n = 1000 -set.seed(10) -x24b <- replicate(24, rnorm(1000)) -par(mfrow = c(3,8), mar = c(0,0,0,0)) -x24bPlot <- apply( - x24b, - 2, - function(x){ - hist(x, col = "grey", xlim = c(-5,5), ylim = c(0,500), breaks = c(-5:5), - main = "", ylab = "", xlab = "", xaxt = "n", yaxt = "n") - abline(v = mean(x), col = "blue", lwd = 2) - abline(v = 0, col = "red", lty = 2, lwd = 2) - } -) - -## distribution of means and SDs from 24 sims N(0,1) with n = 1000 -par(mfrow = c(1,2), mar = c(5,5,1,1)) -hist(apply(x24b, 2, mean), main = "Mean",col = "grey", xlim = c(-1,1)) -abline(v = 0, col = "red", lty = 2, lwd = 2) -hist(apply(x24b, 2, sd), main = "SD",col = "grey", xlim = c(0.6,1.4)) -abline(v = 1, col = "red", lty = 2, lwd = 2) - -## distribution of means and SDs from 1000 sims N(0,1) with n = 10 -set.seed(10) -x1000 <- replicate(1000, rnorm(10)) -par(mfrow = c(1,2), mar = c(5,5,1,1)) -hist(apply(x1000, 2, mean), main = "Mean",col = "grey") -abline(v = 0, col = "red", lty = 2, lwd = 2) -hist(apply(x1000, 2, sd), main = "SD",col = "grey") -abline(v = 1, col = "red", lty = 2, lwd = 2) - - -#~~~~~~~~~ Functions ----- - -# writing a function -## function syntax: -## AwesomeFunctionName <- function(argument1, argument2,…){ -## do stuff here -## } -## The last thing that appears in the 'do stuff here' section is the function's -## "return value" - -# YOUR TURN: write a function that takes input "nrep", replicates '(mean(rnorm(100)))' -# nrep times, and draws a histogram of the results - - - -# YOUR TURN: modify your function -## to draw a histogram of nrep mean(rnorm(n)), where n is another input - - - - -#~~~~~~~~~ Simulating no effect and check alpha ----- - -# YOUR TURN: draw from the same normal distribution twice -## and see if the sample differ from each other -## will they differ significantly in 5% of the nrep? -### Figure out how to do a t.test in R -### Generate two vectors of 10 values drawn from N(0,1) and compare them with a t test -### Figure out how to extract the p-value from that object (HINT use `str` or `names`) -### Write a function simT that generates two vectors of n random normals, compare them with a t test and return the p-value -### Repeat with nrep = 20 and draw a histogram for n = 10 -### Repeat with nrep = 100 and draw a histogram for n = 10 - - - - - - -########################## - -#### repeat function for nrep = 1000 and various n (e.g. 10 and 100) - - - - - - - -#~~~~~~~~~ Simulating an effect and check power ----- - -# we can calculate the power of a t.test for a given sample size using: -power.t.test(n = NULL, delta = 0.5, sd = 1, sig.level = 0.05, power = 0.8) -# the required sample size is 64 per group. - -# YOUR TURN: Use your simulation skills to work out the power of a t-test for a given sample size through simulation. -## Write a function which: -### 1. Draws n values from a random normal distribution with mean 1, and another n values from a normal distribution with mean 2 -### 2. Compares the means of these two samples with a t.test and extracts the p.value -## Then, use that function to replicate the function 1000 times using the parameters used in the power calculation above (that used the power.t.test function). -## Calculate the proportion of p-values that are <0.05 - - - - -#~~~~~~~~~ Simulating for a preregistration ----- - -# YOUR TURN: -## Try to make a dataset that looks like this, using the -## functions `data.frame()`, `sample()`, and `rnorm()` - -# smoking_status lung_cancer sex age -# 1 Yes No M 12.67918 -# 2 Yes Yes F 23.71397 -# 3 No No M 28.87786 -# 4 Yes No F 28.99327 -# 5 Yes Yes F 30.41415 -# 6 No No M 44.60615 - - - - - -# YOUR TURN: -## Run a logistic regression on the data with lung cancer as the outcome and -## adjusting for the other variables. -## You could try something like: -## glm(lung_cancer ~ smoking_status + sex + age, family = binomial(link = "logit"), data = df) -## Why doesn't it work? 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