In graebnerc/DataScienceExercises: Exercises for introductions to R
library(learnr)
library(gradethis)
library(ggplot2)
library(moderndive)
library(ggcheck)
knitr::opts_chunk$set(echo = FALSE)
gradethis_setup(
pass.praise = TRUE, fail.hint = FALSE, fail_code_feedback = FALSE,
fail.encourage = TRUE, maybe_code_feedback = FALSE)
cars2008 <- dplyr::filter(mpg, year==2008)
Content quiz I
Note: SLR stands for Simple Linear Regression.
quiz(
question(
"What does 'simple' in 'Simple linear regression' mean?",
answer(paste0("That we are studying the relationship between two variables"),
correct = TRUE),
answer(paste0("That the estimation equation is rather simple")),
answer(paste0("That there is only a single dependenct variable")),
answer(paste0("That the relationship we assume is linear")),
allow_retry = TRUE, random_answer_order = TRUE),
question(
"Is SLR part of explanatory or exploratory data analysis?",
answer(paste0("Potentially both"),
correct = TRUE),
answer(paste0("Exploratory")),
answer(paste0("Explanatory")),
allow_retry = TRUE, random_answer_order = TRUE),
question(
"Is SLR part of supervised or unsupervised machine learning?",
answer(paste0("Supervised"),
correct = TRUE),
answer(paste0("Unsupervised")),
answer(paste0("Both")),
allow_retry = TRUE, random_answer_order = TRUE),
question(
"What does it mean to 'fit a model'?",
answer(paste0(
"Choose the member of the model family under",
" consideration that describes the data best (according",
"to some pre-specified criterion)."),
correct = TRUE),
answer(paste0(
"Tweaking the model parameters to improve model ",
"performance in the sense of the coefficient of determination.")),
answer(
paste0("Select the model family that is most suitable for the data at hand.")
),
answer(
paste0("Increase the fit of the model by adding more variables.")
),
answer(
paste0("Adjust a model that has been estimated for an existing data ",
"to a new, extended data set.")
),
allow_retry = TRUE, random_answer_order = TRUE),
question(
"What kind of model family are we fitting in the context of SLR?",
answer(paste0("Linear models"),
correct = TRUE),
answer(paste0("Sub-linear models")),
answer(paste0("Linearized models")),
answer(paste0("Simplified models")),
answer(paste0("Models with two free parameters")),
allow_retry = TRUE, random_answer_order = TRUE)
)
Content quiz II
Consider the following typical regression equation:
$$y=\beta_0 + \beta_1 x_1 + \epsilon$$
quiz(
question(
"What is the dependent variable?",
answer(paste0("$y$"),
correct = TRUE),
answer(paste0("$\\beta_0$")),
answer(paste0("$\\beta_1$")),
answer(paste0("$\\epsilon$")),
allow_retry = TRUE, random_answer_order = FALSE),
question(
"What is the intercept of the regression line to be estimated?",
answer(paste0("$y$")),
answer(paste0("$\\beta_0$"),
correct = TRUE),
answer(paste0("$\\beta_1$")),
answer(paste0("$\\epsilon$")),
allow_retry = TRUE, random_answer_order = FALSE),
question(
"What is the slope of the regression line to be estimated?",
answer(paste0("$y$")),
answer(paste0("$\\beta_0$")),
answer(paste0("$\\beta_1$"),
correct = TRUE),
answer(paste0("$\\epsilon$")),
allow_retry = TRUE, random_answer_order = FALSE),
question(
"What is the error term?",
answer(paste0("$y$")),
answer(paste0("$\\beta_0$")),
answer(paste0("$\\beta_1$")),
answer(paste0("$\\epsilon$"),
correct = TRUE),
allow_retry = TRUE, random_answer_order = FALSE),
question(
"What is true about the error term?",
answer(paste0("It absorbs all measured effect on $y$ that are not ",
"captured by $x$."),
correct = TRUE),
answer(paste0("It corresponds to the sum of of squared residuals")),
answer(paste0("It is a synonymon to the term 'residual'")),
answer(paste0("Its inverse is a measure for the goodness of fit of a model")),
allow_retry = TRUE, random_answer_order = TRUE),
question(
"What is a fitted value $\\hat{y}$?",
answer(paste0("The value of $y$ that the model predicts for a given $x$."),
correct = TRUE),
answer(paste0("The part of the RSME that corresponds to the particular $y$")),
answer(paste0("The value that is used to estimate $\\beta_0$ and $\\beta_1$")),
answer(paste0("The value of $y$ that the model predicts for the mean of $x$.")),
allow_retry = TRUE, random_answer_order = TRUE)
)
Content quiz III
quiz(
question(
"What is a cost function in the context of regression analysis?",
answer(paste0(
"A function that measures the difference between actual ",
"and fitted values, conditional on values for the model parameters."),
correct = TRUE),
answer(paste0("A function that measures the computational ",
"complexity of a regression model")),
answer(paste0("A function that measures the cost of replacing ",
"one independent variable for another")),
answer(paste0("A function that computes the squared residuals for ",
"different subsamples of $x$")),
allow_retry = TRUE, random_answer_order = TRUE)
)
Consider the following regression table:
beer_data <- DataScienceExercises::beer
linmod <- lm(consumption~price_liquor, data = beer_data)
moderndive::get_regression_table(linmod)
Note that the variable consumption measures liters of beer consumed per
year, and price_liquor measures the price of other liquor in USD.
quiz(
question(
"What would be the correct interpretation for the estimated coefficient of `price_liquor`?",
answer(paste0(
"For every increase of 1 unit in `price_liquor`, ",
"there is an associated decrease of, on average, 7.78",
" liters of beer consumption."),
correct = TRUE),
answer(paste0(
"For every increase of, on average, 7.78 units in `price_liquor`, ",
"there is an associated decrease of one",
" liter of beer consumption.")),
answer(paste0(
"If `price_liquor` increases by one unit, the beer consumption will, ",
"rise by 7.78 litres")),
answer(paste0(
"For every decrease of 1 unit in `price_liquor`, ",
"there is an associated decrease of, on average, 7.78",
" liters of beer consumption.")),
allow_retry = TRUE, random_answer_order = TRUE),
question(
"What is the idea behind ordinary least squares estimation?",
answer(paste0(
"Derive a mathematical solution to the problem of ",
"minimizing the squared residuals by choosing adequate values for the",
"parameters to be estimated."),
correct = TRUE),
answer(paste0(
"Find the line that minimizes the squared distance between estimated ",
"and actual values by changing intercept and slope until the RMSE is ",
"minimized")),
answer(paste0(
"Compute those fitted values that maximize the ability of the model ",
"to predict")),
answer(paste0(
"Choose those $x$ values that are best suited to fit a linear model."
)),
allow_retry = TRUE, random_answer_order = TRUE),
question(
"What is an estimate?",
answer(paste0(
"The estimate is the result of choosing a particular value for a model, ",
"usually after applying an estimator to data."),
correct = TRUE),
answer(paste0(
"An estimate is way to compute the estimator: its a formula or an algorithm")),
answer(paste0(
"A particular prediction for a fitted value $\\hat{y}$")),
answer(paste0(
"A model that has been estimated")),
allow_retry = TRUE, random_answer_order = TRUE),
question(
"What is an estimator?",
answer(paste0(
"An estimator is way to compute the estimate: its a formula or an algorithm"),
correct = TRUE),
answer(paste0(
"The estimator is the result of choosing a particular value for a model, ",
"usually after applying an estimate to data."
)),
answer(paste0(
"A procedure to minimize the sum of squared residuals"
)),
answer(paste0(
"The procedure to generate estimated values for $y$, i.e. the $\\hat{y}$.")),
allow_retry = TRUE, random_answer_order = TRUE),
question(
"What does the $R^2$ of a fitted model tells us?",
answer(paste0(
"How much variation in the dependent variable is ",
"accounted for by the independent variables of the model."),
correct = TRUE),
answer(paste0(
"How well our model performs in terms of predictive power")),
answer(paste0(
"How much variation in the independent variable is required to explain ",
"the variation in the dependent variable")),
answer(paste0(
"Whether our estimtates are indeed the best ones ",
"we can obtain for the given sample")),
allow_retry = TRUE, random_answer_order = TRUE)
)
Coding exercises
Implementing a linear regression
Consider the following data set called cars2008, which contains information
about the fuel economy of various popular car models:
head(cars2008)
Now analyse the relationship between engine displacement and highway miles
per gallon for the different cars by conducting a linear regression with
highway miles per gallon as the dependent, and engine displacement as the
independent variable.
Note: cars2008 is a subset of the data set mpg, which is built-in into R.
So if you need any information about the data (e.g. variable names), just
type ?mpg into the console.
Hint: To evaluate your result you need to return the regression object you
have created.
lm(____)
lm(formula = ____, ____ = ____)
lm(formula = ____, data = ____)
lm(formula = ____~____, data = ____)
lm(formula = ____~____, data = cars2008)
lm(formula = hwy~____, data = cars2008)
lm(formula = hwy~displ, data = cars2008)
grade_this({
if(!inherits(.result, "lm")){
fail(message = paste(
"Your code should be produce a linear model.",
"Check out the function `lm()`!"))
}
correct_model <- lm(formula = hwy~displ, data = cars2008)
call_made <- str_remove_all(as.character(.result$call), " ")
if (("hwy~displ" %in% call_made) & all.equal(
unname(coefficients(correct_model)),
unname(coefficients(.result)))){
pass()
}
if (("cars2008$hwy~cars2008$displ" %in% call_made) & all.equal(
unname(coefficients(correct_model)),
unname(coefficients(.result))) & "cars2008" %in% call_made){
pass(message = paste(
"This works, but if you use the `data` argument of `lm`,",
"there is no need to refer to the data set in the formula: ",
"`lm(formula = hwy~displ, data = cars2008)`"))
}
if (("cars2008$hwy~cars2008$displ" %in% call_made) & all.equal(
unname(coefficients(correct_model)),
unname(coefficients(.result)))){
pass(message = paste(
"This works, but its better if you use the `data` argument of `lm`,",
"and do not refer to the data set in the formula: ",
"`lm(formula = hwy~displ, data = cars2008)`"))
}
fail("You did not specify the call of `lm()` correctly!")
})
Extracting coefficients
Assume you saved your regression object as linmod_cars. Sometimes you might
want to extract the estimated coefficients. Do this by using the function
coefficients. If you do not know how to do it, use the help function or
Google!
linmod_cars <- lm(formula = hwy~displ, data = cars2008)
coefficients(linmod_cars)
____(____)
____(linmod_cars)
grade_this({
print(.result)
if(!is.double(.result)){
fail(message = paste(
"Your results should be of type `double` but is of type {typeof(.result)}!"))
}
if(!stringr::str_detect(.user_code, "coefficients") ){
fail(message = paste(
"You must make use of the function `coefficients`!"))
}
if(identical(.result, coefficients(linmod_cars))){
pass()
}
fail()
})
Two types of summary tables
There are two ways to extract more information out of your regression object
you should know about: first, the standard way using the function summary(),
and, second, the convenience function moderndive::get_regression_table().
Assume you saved your regression object under the name linmod_cars, as above.
First, extract more information by applying the function summary!
linmod_cars <- lm(formula = hwy~displ, data = cars2008)
____(____)
summary(____)
summary(linmod_cars)
grade_this({
if(!stringr::str_detect(.user_code, "summary") ){
fail(message = paste(
"You must make use of the function `summary()`!"))
}
if(identical(.result, summary(linmod_cars))){
pass()
}
fail(paste("Pass the fitted model saved under the name `linmod_cars`",
"to the function `summary()`!"))
})
Now use the function moderndive::get_regression_table() to get a more
concise overview:
linmod_cars <- lm(formula = hwy~displ, data = cars2008)
____(____)
moderndive::____(____)
moderndive::get_regression_table(____)
moderndive::get_regression_table(linmod_cars)
grade_this({
if(!stringr::str_detect(.user_code, "get_regression_table") ){
fail(message = paste(
"You must make use of the function `moderndive::get_regression_table()`!"))
}
if(identical(.result, moderndive::get_regression_table(linmod_cars))){
pass()
}
fail(paste("Pass the fitted model saved under the name `linmod_cars`",
"to the function `moderndive::get_regression_table()`!"))
})
Extracting the R squared
In the lecture you learned about the $R^2$ of a regression as a measure for
the share of explained variation in the dependent variable. Extract the $R^2$
from the regression object linmod_cars.
Hint: The $R^2$ is contained in the object produced by summary(). Thus, `
you first need to compute the summary object, and then extract the $R^2$ from
there. If you are stuck, search for hints in the internet!
linmod_cars <- lm(formula = hwy~displ, data = cars2008)
linmod_cars_summary <- ____(____)
linmod_cars_summary____
linmod_cars_summary <- summary(____)
linmod_cars_summary____
linmod_cars_summary <- summary(linmod_cars)
linmod_cars_summary____
linmod_cars_summary <- summary(linmod_cars)
linmod_cars_summary[[____]]
linmod_cars_summary <- summary(linmod_cars)
linmod_cars_summary[["r.squared"]]
grade_this({
linmod_cars_summary <- summary(linmod_cars)
if(!is.double(.result)){
fail(message = paste(
"Your results should be of type `double` but is of type {typeof(.result)}!"))
}
if(!stringr::str_detect(.user_code, "summary") ){
fail(message = paste(
"You must make use of the function `summary` during your solution!"))
}
if(!stringr::str_detect(.user_code, "r.squared") ){
fail(message = paste(
"The function `summary` produces a list. One of its members is",
"the $R^2$. If you cannot find it, maybe check out the structure",
"of the list using `str()`!"))
}
if(identical(.result, linmod_cars_summary[["r.squared"]])){
pass()
}
fail()
})
Visualize a regression
A good way to visualize your regression model is by adding a regression line
into a ggplot2-object. You can achieve this by adding the geom
geom_smooth(method='lm') to your plot. Try this by making a scatter plot of
the data set cars2008, where engine displacement appears on the x-axis and
highway miles per gallon on the y-axis.
Note: This is a very useful command when you explore your data and ask
yourself whether a linear model is adequate in the first place!
ggplot(____) +
geom_____() +
geom_____(____)
ggplot(data = ____, mapping = ____) +
geom_____() +
geom_____(____)
ggplot(data = cars2008, mapping = aes(x=____, y=____)) +
geom_____() +
geom_____(____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) +
geom_____() +
geom_____(____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) +
geom_point() +
geom_____(____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) +
geom_point() +
geom_smooth(____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) +
geom_point() +
geom_smooth(method = ____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) +
geom_point() +
geom_smooth(method = ____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) +
geom_point() +
geom_smooth(method = "lm") +
theme_bw()
grade_this({
fail_if(!ggcheck::is_ggplot(.result),
message = paste0(
"You did not define a `ggplot` object. Use the function ",
"`ggplot2::ggplot()`. ",
"Did you maybe forget to call and render the plot?"
)
)
fail_if(!ggcheck::uses_data(.result, cars2008),
message = paste0(
"You should use the data set `cars2008`. You can pass ",
"it to the argument `data` of `ggplot2::ggplot()`."
)
)
fail_if(!uses_mappings(.result, aes(x=displ, y=hwy), exact = TRUE),
message = paste0(
"You should map the variable `displ` to the x-axis, and the ",
"variable `hwy` to the y-axis! Use the argument `mapping` ",
"of the `ggplot2::ggplot()` function, as well as `ggplot2::aes()`."
)
)
fail_if(!ggcheck::uses_geoms(.result, "point", exact = FALSE),
message = paste0(
"To produce a scatterplot you must use the geom 'point'."
)
)
fail_if(!ggcheck::uses_geoms(.result, "smooth", exact = FALSE),
message = paste0(
"To add the regression line you need to use `geom_smooth()`."
)
)
fail_if(!ggcheck::uses_geom_param(.result, "smooth", list(method = "lm")),
message = paste0(
"To fit a linear model with `geom_smooth()` you need to ",
"set the argument `method` to `'lm'`!"
)
)
pass_if(!stringr::str_detect(.user_code, "theme_"),
message = paste("But remember that the default ggplot ",
"always looks a bit ugly. Cheer your result up by ",
"using, e.g., `theme_bw()`!"))
pass()
}
)
graebnerc/DataScienceExercises documentation built on April 11, 2025, 7:57 p.m.
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library(learnr) library(gradethis) library(ggplot2) library(moderndive) library(ggcheck) knitr::opts_chunk$set(echo = FALSE) gradethis_setup( pass.praise = TRUE, fail.hint = FALSE, fail_code_feedback = FALSE, fail.encourage = TRUE, maybe_code_feedback = FALSE) cars2008 <- dplyr::filter(mpg, year==2008)
Content quiz I
Note: SLR stands for Simple Linear Regression.
quiz( question( "What does 'simple' in 'Simple linear regression' mean?", answer(paste0("That we are studying the relationship between two variables"), correct = TRUE), answer(paste0("That the estimation equation is rather simple")), answer(paste0("That there is only a single dependenct variable")), answer(paste0("That the relationship we assume is linear")), allow_retry = TRUE, random_answer_order = TRUE), question( "Is SLR part of explanatory or exploratory data analysis?", answer(paste0("Potentially both"), correct = TRUE), answer(paste0("Exploratory")), answer(paste0("Explanatory")), allow_retry = TRUE, random_answer_order = TRUE), question( "Is SLR part of supervised or unsupervised machine learning?", answer(paste0("Supervised"), correct = TRUE), answer(paste0("Unsupervised")), answer(paste0("Both")), allow_retry = TRUE, random_answer_order = TRUE), question( "What does it mean to 'fit a model'?", answer(paste0( "Choose the member of the model family under", " consideration that describes the data best (according", "to some pre-specified criterion)."), correct = TRUE), answer(paste0( "Tweaking the model parameters to improve model ", "performance in the sense of the coefficient of determination.")), answer( paste0("Select the model family that is most suitable for the data at hand.") ), answer( paste0("Increase the fit of the model by adding more variables.") ), answer( paste0("Adjust a model that has been estimated for an existing data ", "to a new, extended data set.") ), allow_retry = TRUE, random_answer_order = TRUE), question( "What kind of model family are we fitting in the context of SLR?", answer(paste0("Linear models"), correct = TRUE), answer(paste0("Sub-linear models")), answer(paste0("Linearized models")), answer(paste0("Simplified models")), answer(paste0("Models with two free parameters")), allow_retry = TRUE, random_answer_order = TRUE) )
Content quiz II
Consider the following typical regression equation:
$$y=\beta_0 + \beta_1 x_1 + \epsilon$$
quiz( question( "What is the dependent variable?", answer(paste0("$y$"), correct = TRUE), answer(paste0("$\\beta_0$")), answer(paste0("$\\beta_1$")), answer(paste0("$\\epsilon$")), allow_retry = TRUE, random_answer_order = FALSE), question( "What is the intercept of the regression line to be estimated?", answer(paste0("$y$")), answer(paste0("$\\beta_0$"), correct = TRUE), answer(paste0("$\\beta_1$")), answer(paste0("$\\epsilon$")), allow_retry = TRUE, random_answer_order = FALSE), question( "What is the slope of the regression line to be estimated?", answer(paste0("$y$")), answer(paste0("$\\beta_0$")), answer(paste0("$\\beta_1$"), correct = TRUE), answer(paste0("$\\epsilon$")), allow_retry = TRUE, random_answer_order = FALSE), question( "What is the error term?", answer(paste0("$y$")), answer(paste0("$\\beta_0$")), answer(paste0("$\\beta_1$")), answer(paste0("$\\epsilon$"), correct = TRUE), allow_retry = TRUE, random_answer_order = FALSE), question( "What is true about the error term?", answer(paste0("It absorbs all measured effect on $y$ that are not ", "captured by $x$."), correct = TRUE), answer(paste0("It corresponds to the sum of of squared residuals")), answer(paste0("It is a synonymon to the term 'residual'")), answer(paste0("Its inverse is a measure for the goodness of fit of a model")), allow_retry = TRUE, random_answer_order = TRUE), question( "What is a fitted value $\\hat{y}$?", answer(paste0("The value of $y$ that the model predicts for a given $x$."), correct = TRUE), answer(paste0("The part of the RSME that corresponds to the particular $y$")), answer(paste0("The value that is used to estimate $\\beta_0$ and $\\beta_1$")), answer(paste0("The value of $y$ that the model predicts for the mean of $x$.")), allow_retry = TRUE, random_answer_order = TRUE) )
Content quiz III
quiz( question( "What is a cost function in the context of regression analysis?", answer(paste0( "A function that measures the difference between actual ", "and fitted values, conditional on values for the model parameters."), correct = TRUE), answer(paste0("A function that measures the computational ", "complexity of a regression model")), answer(paste0("A function that measures the cost of replacing ", "one independent variable for another")), answer(paste0("A function that computes the squared residuals for ", "different subsamples of $x$")), allow_retry = TRUE, random_answer_order = TRUE) )
Consider the following regression table:
beer_data <- DataScienceExercises::beer linmod <- lm(consumption~price_liquor, data = beer_data) moderndive::get_regression_table(linmod)
Note that the variable consumption measures liters of beer consumed per
year, and price_liquor measures the price of other liquor in USD.
quiz( question( "What would be the correct interpretation for the estimated coefficient of `price_liquor`?", answer(paste0( "For every increase of 1 unit in `price_liquor`, ", "there is an associated decrease of, on average, 7.78", " liters of beer consumption."), correct = TRUE), answer(paste0( "For every increase of, on average, 7.78 units in `price_liquor`, ", "there is an associated decrease of one", " liter of beer consumption.")), answer(paste0( "If `price_liquor` increases by one unit, the beer consumption will, ", "rise by 7.78 litres")), answer(paste0( "For every decrease of 1 unit in `price_liquor`, ", "there is an associated decrease of, on average, 7.78", " liters of beer consumption.")), allow_retry = TRUE, random_answer_order = TRUE), question( "What is the idea behind ordinary least squares estimation?", answer(paste0( "Derive a mathematical solution to the problem of ", "minimizing the squared residuals by choosing adequate values for the", "parameters to be estimated."), correct = TRUE), answer(paste0( "Find the line that minimizes the squared distance between estimated ", "and actual values by changing intercept and slope until the RMSE is ", "minimized")), answer(paste0( "Compute those fitted values that maximize the ability of the model ", "to predict")), answer(paste0( "Choose those $x$ values that are best suited to fit a linear model." )), allow_retry = TRUE, random_answer_order = TRUE), question( "What is an estimate?", answer(paste0( "The estimate is the result of choosing a particular value for a model, ", "usually after applying an estimator to data."), correct = TRUE), answer(paste0( "An estimate is way to compute the estimator: its a formula or an algorithm")), answer(paste0( "A particular prediction for a fitted value $\\hat{y}$")), answer(paste0( "A model that has been estimated")), allow_retry = TRUE, random_answer_order = TRUE), question( "What is an estimator?", answer(paste0( "An estimator is way to compute the estimate: its a formula or an algorithm"), correct = TRUE), answer(paste0( "The estimator is the result of choosing a particular value for a model, ", "usually after applying an estimate to data." )), answer(paste0( "A procedure to minimize the sum of squared residuals" )), answer(paste0( "The procedure to generate estimated values for $y$, i.e. the $\\hat{y}$.")), allow_retry = TRUE, random_answer_order = TRUE), question( "What does the $R^2$ of a fitted model tells us?", answer(paste0( "How much variation in the dependent variable is ", "accounted for by the independent variables of the model."), correct = TRUE), answer(paste0( "How well our model performs in terms of predictive power")), answer(paste0( "How much variation in the independent variable is required to explain ", "the variation in the dependent variable")), answer(paste0( "Whether our estimtates are indeed the best ones ", "we can obtain for the given sample")), allow_retry = TRUE, random_answer_order = TRUE) )
Coding exercises
Implementing a linear regression
Consider the following data set called cars2008, which contains information
about the fuel economy of various popular car models:
head(cars2008)
Now analyse the relationship between engine displacement and highway miles per gallon for the different cars by conducting a linear regression with highway miles per gallon as the dependent, and engine displacement as the independent variable.
Note: cars2008 is a subset of the data set mpg, which is built-in into R.
So if you need any information about the data (e.g. variable names), just
type ?mpg into the console.
Hint: To evaluate your result you need to return the regression object you have created.
lm(____)
lm(formula = ____, ____ = ____)
lm(formula = ____, data = ____)
lm(formula = ____~____, data = ____)
lm(formula = ____~____, data = cars2008)
lm(formula = hwy~____, data = cars2008)
lm(formula = hwy~displ, data = cars2008)
grade_this({ if(!inherits(.result, "lm")){ fail(message = paste( "Your code should be produce a linear model.", "Check out the function `lm()`!")) } correct_model <- lm(formula = hwy~displ, data = cars2008) call_made <- str_remove_all(as.character(.result$call), " ") if (("hwy~displ" %in% call_made) & all.equal( unname(coefficients(correct_model)), unname(coefficients(.result)))){ pass() } if (("cars2008$hwy~cars2008$displ" %in% call_made) & all.equal( unname(coefficients(correct_model)), unname(coefficients(.result))) & "cars2008" %in% call_made){ pass(message = paste( "This works, but if you use the `data` argument of `lm`,", "there is no need to refer to the data set in the formula: ", "`lm(formula = hwy~displ, data = cars2008)`")) } if (("cars2008$hwy~cars2008$displ" %in% call_made) & all.equal( unname(coefficients(correct_model)), unname(coefficients(.result)))){ pass(message = paste( "This works, but its better if you use the `data` argument of `lm`,", "and do not refer to the data set in the formula: ", "`lm(formula = hwy~displ, data = cars2008)`")) } fail("You did not specify the call of `lm()` correctly!") })
Extracting coefficients
Assume you saved your regression object as linmod_cars. Sometimes you might
want to extract the estimated coefficients. Do this by using the function
coefficients. If you do not know how to do it, use the help function or
Google!
linmod_cars <- lm(formula = hwy~displ, data = cars2008)
coefficients(linmod_cars)
____(____)
____(linmod_cars)
grade_this({ print(.result) if(!is.double(.result)){ fail(message = paste( "Your results should be of type `double` but is of type {typeof(.result)}!")) } if(!stringr::str_detect(.user_code, "coefficients") ){ fail(message = paste( "You must make use of the function `coefficients`!")) } if(identical(.result, coefficients(linmod_cars))){ pass() } fail() })
Two types of summary tables
There are two ways to extract more information out of your regression object
you should know about: first, the standard way using the function summary(),
and, second, the convenience function moderndive::get_regression_table().
Assume you saved your regression object under the name linmod_cars, as above.
First, extract more information by applying the function summary!
linmod_cars <- lm(formula = hwy~displ, data = cars2008)
____(____)
summary(____)
summary(linmod_cars)
grade_this({ if(!stringr::str_detect(.user_code, "summary") ){ fail(message = paste( "You must make use of the function `summary()`!")) } if(identical(.result, summary(linmod_cars))){ pass() } fail(paste("Pass the fitted model saved under the name `linmod_cars`", "to the function `summary()`!")) })
Now use the function moderndive::get_regression_table() to get a more
concise overview:
linmod_cars <- lm(formula = hwy~displ, data = cars2008)
____(____)
moderndive::____(____)
moderndive::get_regression_table(____)
moderndive::get_regression_table(linmod_cars)
grade_this({ if(!stringr::str_detect(.user_code, "get_regression_table") ){ fail(message = paste( "You must make use of the function `moderndive::get_regression_table()`!")) } if(identical(.result, moderndive::get_regression_table(linmod_cars))){ pass() } fail(paste("Pass the fitted model saved under the name `linmod_cars`", "to the function `moderndive::get_regression_table()`!")) })
Extracting the R squared
In the lecture you learned about the $R^2$ of a regression as a measure for
the share of explained variation in the dependent variable. Extract the $R^2$
from the regression object linmod_cars.
Hint: The $R^2$ is contained in the object produced by summary(). Thus, `
you first need to compute the summary object, and then extract the $R^2$ from
there. If you are stuck, search for hints in the internet!
linmod_cars <- lm(formula = hwy~displ, data = cars2008)
linmod_cars_summary <- ____(____) linmod_cars_summary____
linmod_cars_summary <- summary(____) linmod_cars_summary____
linmod_cars_summary <- summary(linmod_cars) linmod_cars_summary____
linmod_cars_summary <- summary(linmod_cars) linmod_cars_summary[[____]]
linmod_cars_summary <- summary(linmod_cars) linmod_cars_summary[["r.squared"]]
grade_this({ linmod_cars_summary <- summary(linmod_cars) if(!is.double(.result)){ fail(message = paste( "Your results should be of type `double` but is of type {typeof(.result)}!")) } if(!stringr::str_detect(.user_code, "summary") ){ fail(message = paste( "You must make use of the function `summary` during your solution!")) } if(!stringr::str_detect(.user_code, "r.squared") ){ fail(message = paste( "The function `summary` produces a list. One of its members is", "the $R^2$. If you cannot find it, maybe check out the structure", "of the list using `str()`!")) } if(identical(.result, linmod_cars_summary[["r.squared"]])){ pass() } fail() })
Visualize a regression
A good way to visualize your regression model is by adding a regression line
into a ggplot2-object. You can achieve this by adding the geom
geom_smooth(method='lm') to your plot. Try this by making a scatter plot of
the data set cars2008, where engine displacement appears on the x-axis and
highway miles per gallon on the y-axis.
Note: This is a very useful command when you explore your data and ask yourself whether a linear model is adequate in the first place!
ggplot(____) + geom_____() + geom_____(____)
ggplot(data = ____, mapping = ____) + geom_____() + geom_____(____)
ggplot(data = cars2008, mapping = aes(x=____, y=____)) + geom_____() + geom_____(____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) + geom_____() + geom_____(____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) + geom_point() + geom_____(____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) + geom_point() + geom_smooth(____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) + geom_point() + geom_smooth(method = ____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) + geom_point() + geom_smooth(method = ____)
ggplot(data = cars2008, mapping = aes(x=displ, y=hwy)) + geom_point() + geom_smooth(method = "lm") + theme_bw()
grade_this({ fail_if(!ggcheck::is_ggplot(.result), message = paste0( "You did not define a `ggplot` object. Use the function ", "`ggplot2::ggplot()`. ", "Did you maybe forget to call and render the plot?" ) ) fail_if(!ggcheck::uses_data(.result, cars2008), message = paste0( "You should use the data set `cars2008`. You can pass ", "it to the argument `data` of `ggplot2::ggplot()`." ) ) fail_if(!uses_mappings(.result, aes(x=displ, y=hwy), exact = TRUE), message = paste0( "You should map the variable `displ` to the x-axis, and the ", "variable `hwy` to the y-axis! Use the argument `mapping` ", "of the `ggplot2::ggplot()` function, as well as `ggplot2::aes()`." ) ) fail_if(!ggcheck::uses_geoms(.result, "point", exact = FALSE), message = paste0( "To produce a scatterplot you must use the geom 'point'." ) ) fail_if(!ggcheck::uses_geoms(.result, "smooth", exact = FALSE), message = paste0( "To add the regression line you need to use `geom_smooth()`." ) ) fail_if(!ggcheck::uses_geom_param(.result, "smooth", list(method = "lm")), message = paste0( "To fit a linear model with `geom_smooth()` you need to ", "set the argument `method` to `'lm'`!" ) ) pass_if(!stringr::str_detect(.user_code, "theme_"), message = paste("But remember that the default ggplot ", "always looks a bit ugly. Cheer your result up by ", "using, e.g., `theme_bw()`!")) pass() } )
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