# 1 Hintergrund

Diese Übung bezieht sich auf ISRS, Kap. 6.3.

# 2 Pakete

library(tidyverse)  # data wrangling
#library(broom)  # tidy Regressionsoutput
library(skimr)  # EDA
library(moderndive)  # Komfort

Auf dieser Seite sind die Daten zu finden.

d <- read_csv("https://www.openintro.org/data/csv/mariokart.csv")

(“d” wie Daten.)

Wir werfen einen Blick in die Daten:

glimpse(d)
#> Rows: 143
#> Columns: 12
#> $id <dbl> 150377422259, 260483376854, 320432342985, 280405224677, 1… #>$ duration    <dbl> 3, 7, 3, 3, 1, 3, 1, 1, 3, 7, 1, 1, 1, 1, 7, 7, 3, 3, 1, …
#> $n_bids <dbl> 20, 13, 16, 18, 20, 19, 13, 15, 29, 8, 15, 15, 13, 16, 6,… #>$ cond        <chr> "new", "used", "new", "new", "new", "new", "used", "new",…
#> $start_pr <dbl> 0.99, 0.99, 0.99, 0.99, 0.01, 0.99, 0.01, 1.00, 0.99, 19.… #>$ ship_pr     <dbl> 4.00, 3.99, 3.50, 0.00, 0.00, 4.00, 0.00, 2.99, 4.00, 4.0…
#> $total_pr <dbl> 51.55, 37.04, 45.50, 44.00, 71.00, 45.00, 37.02, 53.99, 4… #>$ ship_sp     <chr> "standard", "firstClass", "firstClass", "standard", "medi…
#> $seller_rate <dbl> 1580, 365, 998, 7, 820, 270144, 7284, 4858, 27, 201, 4858… #>$ stock_photo <chr> "yes", "yes", "no", "yes", "yes", "yes", "yes", "yes", "y…
#> $wheels <dbl> 1, 1, 1, 1, 2, 0, 0, 2, 1, 1, 2, 2, 2, 2, 1, 0, 1, 1, 2, … #>$ title       <chr> "~~ Wii MARIO KART &amp; WHEEL ~ NINTENDO Wii ~ BRAND NEW…

Oder lieber so:

skim(d)
 Name d Number of rows 143 Number of columns 12 _______________________ Column type frequency: character 4 numeric 8 ________________________ Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
cond 0 1.00 3 4 0 2 0
ship_sp 0 1.00 5 10 0 8 0
stock_photo 0 1.00 2 3 0 2 0
title 1 0.99 13 59 0 80 0

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
id 0 1 2.235290e+11 8.809543e+10 1.104392e+11 1.403506e+11 2.204911e+11 2.953551e+11 4.000775e+11 ▇▃▅▅▃
duration 0 1 3.770000e+00 2.590000e+00 1.000000e+00 1.000000e+00 3.000000e+00 7.000000e+00 1.000000e+01 ▇▅▂▆▁
n_bids 0 1 1.354000e+01 5.880000e+00 1.000000e+00 1.000000e+01 1.400000e+01 1.700000e+01 2.900000e+01 ▂▅▇▃▁
start_pr 0 1 8.780000e+00 1.507000e+01 1.000000e-02 9.900000e-01 1.000000e+00 1.000000e+01 6.995000e+01 ▇▁▁▁▁
ship_pr 0 1 3.140000e+00 3.210000e+00 0.000000e+00 0.000000e+00 3.000000e+00 4.000000e+00 2.551000e+01 ▇▁▁▁▁
total_pr 0 1 4.988000e+01 2.569000e+01 2.898000e+01 4.117000e+01 4.650000e+01 5.399000e+01 3.265100e+02 ▇▁▁▁▁
seller_rate 0 1 1.589842e+04 5.184032e+04 0.000000e+00 1.090000e+02 8.200000e+02 4.858000e+03 2.701440e+05 ▇▁▁▁▁
wheels 0 1 1.150000e+00 8.500000e-01 0.000000e+00 0.000000e+00 1.000000e+00 2.000000e+00 4.000000e+00 ▆▇▇▁▁

# 4 Fehlende Werte

Fehlende Werte können Probleme bereiten. Entfernen wir einfach alle fehlenden Werte, es sind ja nicht so viele.

d_nona <- d %>%   # nona wie "no NA", keine fehlenden Werte
drop_na()

# 5 Modell 1

Betrachten wir dieses Modell:

lm1 <- lm(total_pr ~ wheels, data = d_nona)
get_regression_summaries(lm1)
#> # A tibble: 1 x 9
#>   r_squared adj_r_squared   mse  rmse sigma statistic p_value    df  nobs
#>       <dbl>         <dbl> <dbl> <dbl> <dbl>     <dbl>   <dbl> <dbl> <dbl>
#> 1      0.11         0.103  587.  24.2  24.4      17.3       0     1   142
get_regression_table(lm1)
#> # A tibble: 2 x 7
#>   term      estimate std_error statistic p_value lower_ci upper_ci
#>   <chr>        <dbl>     <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
#> 1 intercept     38.4      3.44     11.1        0    31.6      45.2
#> 2 wheels        10.1      2.43      4.15       0     5.28     14.9

# 6 Überprüfen der Annahmen

Die vorhergesagten Werte und die Residuen kann man sich so ausgeben lassen:

get_regression_points(lm1)
#> # A tibble: 142 x 5
#>       ID total_pr wheels total_pr_hat residual
#>    <int>    <dbl>  <dbl>        <dbl>    <dbl>
#>  1     1     51.6      1         48.5     3.09
#>  2     2     37.0      1         48.5   -11.4
#>  3     3     45.5      1         48.5    -2.96
#>  4     4     44        1         48.5    -4.46
#>  5     5     71        2         58.5    12.5
#>  6     6     45        0         38.4     6.62
#>  7     7     37.0      0         38.4    -1.36
#>  8     8     54.0      2         58.5    -4.56
#>  9     9     47        1         48.5    -1.46
#> 10    10     50        1         48.5     1.54
#> # … with 132 more rows

## 6.1 Linearität

get_regression_points(lm1) %>%
ggplot(aes(x = wheels, y = residual)) +
geom_point()

Hier böte es sich an, zunächst auf Ausreißer hin zu kontrollieren.

## 6.2 Varianzgleichheit der Residuen

get_regression_points(lm1) %>%
ggplot(aes(x = total_pr_hat, y = abs(residual))) +
geom_point()

## 6.3 Normalverteilung der Residuen

get_regression_points(lm1) %>%
ggplot(aes(x = residual)) +
geom_density()

# 7 Reproducibility

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