Solution to the fit model to artificial data exercise

1 Script with output

## load packages
library(dplyr)
library(tidyr)
library(ggplot2)
library(ggfortify)

## theme for ggplot
theme_set(theme_classic())
theme_update(text = element_text(size = 14))

## create dataset
alpha <- 200
beta <- -3
sigma_val <- 10
nvalues <- 100

df <- tibble(
    x = seq(0, 20, length = nvalues),
    y = alpha + beta * x + rnorm(nvalues, mean = 0, sd = sigma_val)) 

## fit model
lm1 <- lm(y ~ x, data = df)

## check assumptions
autoplot(lm1, which = 1:2)

## check recovered parameters
lm1

Call:
lm(formula = y ~ x, data = df)

Coefficients:
(Intercept)            x  
    203.948       -3.315  

sigma(lm1)

[1] 10.64064

## plot predictions
df_pred <- tibble(x = seq(min(df$x), max(df$x), length = 100)) %>%
    bind_cols(predict(lm1, newdata = ., 
                    interval = "confidence")) %>%
    rename(conf_low = lwr, conf_up = upr) %>%
    select(-fit) %>%
    bind_cols(predict(lm1, newdata = ., 
                  interval = "prediction")) %>%
    rename(pred_low = lwr, pred_up = upr) 

ggplot(df, aes(x, y)) +
    geom_ribbon(aes(y = fit, ymin = conf_low, ymax = conf_up), 
                data = df_pred, fill = "red", alpha = 0.2) +
    geom_ribbon(aes(y = fit, ymin = pred_low, ymax = pred_up), 
                data = df_pred, 
                alpha = 0.2) +
    geom_line(aes(y = fit), data = df_pred,
              color = "red", linewidth = 1.5) +
    geom_point(size = 4, alpha = 0.5) 

2 Script for copy-pasting

## load packages
library(dplyr)
library(tidyr)
library(ggplot2)
library(ggfortify)

## theme for ggplot
theme_set(theme_classic())
theme_update(text = element_text(size = 14))

## create dataset
alpha <- 200
beta <- -3
sigma_val <- 10
nvalues <- 100

df <- tibble(
    x = seq(0, 20, length = nvalues),
    y = alpha + beta * x + rnorm(nvalues, mean = 0, sd = sigma_val)) 

## fit model
lm1 <- lm(y ~ x, data = df)

## check assumptions
autoplot(lm1, which = 1:2)

## check recovered parameters
lm1
sigma(lm1)

## plot predictions
df_pred <- tibble(x = seq(min(df$x), max(df$x), length = 100)) %>%
    bind_cols(predict(lm1, newdata = ., 
                    interval = "confidence")) %>%
    rename(conf_low = lwr, conf_up = upr) %>%
    select(-fit) %>%
    bind_cols(predict(lm1, newdata = ., 
                  interval = "prediction")) %>%
    rename(pred_low = lwr, pred_up = upr) 

ggplot(df, aes(x, y)) +
    geom_ribbon(aes(y = fit, ymin = conf_low, ymax = conf_up), 
                data = df_pred, fill = "red", alpha = 0.2) +
    geom_ribbon(aes(y = fit, ymin = pred_low, ymax = pred_up), 
                data = df_pred, 
                alpha = 0.2) +
    geom_line(aes(y = fit), data = df_pred,
              color = "red", linewidth = 1.5) +
    geom_point(size = 4, alpha = 0.5)