In colinbousige/tutor: Interactive tutorials for learning R

# rmarkdown::run("fits.Rmd")
library(learnr)
library(tutor)
library(tidyverse)
gradethis::gradethis_setup()

Exercise 1

Let's say we have these data in a tibble called df and want to fit them with a linear model:

x <- 1:10
y <- .5*x + runif(length(x))*.8
df <- tibble(x,y)
ggplot(df, aes(x = x, y = y)) +
    expand_limits(x=0,y=0)+
    geom_point()

Let's fit it with free parameters:

head(df,2)
fit <- lm(data = ___, ___ ~ ___)
# Print the fit summary
summary(___)
# Let's plot the result
df %>%
    ggplot(aes(x = x, y = y)) +
    expand_limits(x = 0, y = 0) +
    geom_point()+
    geom_line(aes(y = predict(fit)), col="red")

head(df, 2)
fit <- lm(data = df, y ~ x)
# Print the fit summary
summary(fit)
# Let's plot the result
df %>%
    ggplot(aes(x = x, y = y)) +
    expand_limits(x = 0, y = 0) +
    geom_point() +
    geom_line(aes(y = predict(fit)), col = "red")

grade_code()

Now let's say we want to fix the intercept in 0 or in 1, how would you do it?

fit_fixed0 <- lm(data = ___, ___ ~ ___)
fit_fixed1 <- lm(data = ___, ___ ~ ___)
# Let's plot the result and compare it to the previous one
df %>%
    ggplot(aes(x = x, y = y)) +
    expand_limits(x = 0, y = 0) +
    geom_point() +
    geom_line(aes(y = predict(fit), col = "Free")) +
    geom_line(aes(y = predict(fit_fixed0), col = "Fixed 0")) +
    geom_line(aes(y = 1 + coef(fit_fixed1) * x, col = "Fixed 1"))

fit_fixed0 <- lm(data=df, y ~ x+0)
fit_fixed1 <- lm(data=df, y-1 ~ x+0)
# Let's plot the result and compare it to the previous one
df %>%
    ggplot(aes(x = x, y = y)) +
    expand_limits(x = 0, y = 0) +
    geom_point() +
    geom_line(aes(y = predict(fit), col = "Free")) +
    geom_line(aes(y = predict(fit_fixed0), col = "Fixed 0")) +
    geom_line(aes(y = 1 + coef(fit_fixed1) * x, col = "Fixed 1"))

grade_code()

Exercise 2

Load the tidyverse library, then read the file tutor_examples("exo_fit.txt") into a tibble{.R} called tofit.

library(___)
# tutor_examples("exo_fit.txt")
tofit <- ___
tofit

library(tidyverse)
tofit <- read_table(tutor_examples("exo_fit.txt"))

grade_code()

Plot all columns as a function of x to see your data. For this, use on-the-fly the function pivot_longer(){.R} to turn the tibble into a tidy one:

tofit <- read_table(tutor_examples("exo_fit.txt"))

tofit %>% 
    pivot_longer(cols = ___, # what column do we keep? cols = -this_column
                 values_to = ___, # name of the column gathering the values
                 names_to = ___ # names of the column gathering the variable names
                 ) %>% 
    ggplot(aes(x = ___, y = ___)) + # what columns contain the x and y values?
        geom_point() + # plot with points
        facet____(~ ___, scales = ___) # put the plots on a grid varying according to a column, with free scales

tofit %>% 
    pivot_longer(cols = -x,
                 values_to = "y",
                 names_to = "variable"
                 ) %>% 
    ggplot(aes(x = x, y = y)) +
        geom_point() +
        facet_wrap(~variable, scales="free")

grade_code()

Using lm(){.R} or nls(){.R} fit each column as a function of x and display the "experimental" data and the fit on the same graph. + Tip: Take a look at the function dnorm(){.R} to define a Gaussian

tofit <- read_table(tutor_examples("exo_fit.txt"))

fit_y <- lm(data = ___, ___) # what is the dataframe? what do we fit against what?
# predict(fit_y)
# coef(fit_y)
P1 <- ___ %>% # what dataframe are we working on?
    ggplot(aes(x = ___, y = ___)) + # what are the x and y values of the plot?
        geom____() + # plot the data to fit with points
        geom_line(___, col = ___) # how do we add the fitted values with a red line?
# # # # # # # # # # # # # # # # # # # # # # #
fit_z <- nls(data = ___, # the data
    ___, # the function
    start = list(___) # the list of starting parameters
)
P2 <- ___ %>% 
    ggplot(___) +
        ___
# # # # # # # # # # # # # # # # # # # # # # #
fit_w <- lm(___) # how can we fit w with a linear function?
P3 <- ___ %>% 
    ggplot(___) +
        ___
# # # # # # # # # # # # # # # # # # # # # # #
fit_u <- lm(___) # how can we fit u with a linear function?
P4 <- ___ %>% 
    ggplot(___) +
        ___
# # # # # # # # # # # # # # # # # # # # # # #
fit_s <- ___ # linear or non-linear fit?
P5 <- ___ %>% 
    ggplot(___) +
        ___
# # # # # # # # # # # # # # # # # # # # # # #
library(patchwork) # to gather the plots on a grid easily
P1 + P2 + P3 + P4 + P5 # plot on a grid

fit_y <- lm(data = tofit, y ~ x)
P1 <- tofit %>% ggplot(aes(x = x, y = y)) +
    geom_point() +
    geom_line(aes(y = predict(fit_y)), col = "red")
# # # # # # # # # # # # # # # # # # # # # # # 
fit_z <- nls(data = tofit,
    z ~ A * dnorm(x, mean, sd),
    start = list(
        A = 8,
        mean = 4,
        sd = 1
    ))
P2 <- tofit %>% ggplot(aes(x = x, y = z)) +
    geom_point() +
    geom_line(aes(y = predict(fit_z)), col = "red")
# # # # # # # # # # # # # # # # # # # # # # #
fit_w <- lm(data = tofit, log(w) ~ x)
P3 <- tofit %>% ggplot(aes(x = x, y = log(w))) +
    geom_point() +
    geom_line(aes(y = predict(fit_w)), col = "red")
# # # # # # # # # # # # # # # # # # # # # # #
fit_u <- lm(data = tofit, exp(u) ~ x)
P4 <- tofit %>% ggplot(aes(x = x, y = exp(u))) +
    geom_point() +
    geom_line(aes(y = predict(fit_u)), col = "red")
# # # # # # # # # # # # # # # # # # # # # # #
fit_s <- lm(data = tofit, log(s) ~ x)
P5 <- tofit %>% ggplot(aes(x = x, y = log(s))) +
    geom_point() +
    geom_line(aes(y = predict(fit_s)), col = "red")
# # # # # # # # # # # # # # # # # # # # # # #
library(patchwork)
P1 + P2 + P3 + P4 + P5