Problem Set Stats Bootcamp - class 12

Hypothesis Testing

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biochem <- read_tsv("http://mtweb.cs.ucl.ac.uk/HSMICE/PHENOTYPES/Biochemistry.txt", show_col_types = FALSE) |>
  janitor::clean_names()

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# simplify names a bit more
colnames(biochem) <- gsub(pattern = "biochem_", replacement = "", colnames(biochem))

# we are going to simplify this a bit and only keep some columns
keep <- colnames(biochem)[c(1, 6, 9, 14, 15, 24:28)]
biochem <- biochem[, keep]

# get weights for each individual mouse
# careful: did not come with column names
weight <- read_tsv("http://mtweb.cs.ucl.ac.uk/HSMICE/PHENOTYPES/weight", col_names = F, show_col_types = FALSE)

# add column names
colnames(weight) <- c("subject_name", "weight")

# add weight to biochem table and get rid of NAs
# rename gender to sex
b <- inner_join(biochem, weight, by = "subject_name") |>
  na.omit() |>
  rename(sex = gender)

Problem # 1

Can mouse sex explain mouse cholesterol? {.smaller}

STEP 1: Null hypothesis and variable specification

\(\mathcal{H}_0:\)

?? is the response variable

?? is the explanatory variable

STEP 2: Fit linear model and examine results

Fit summary:

Coefficient summary:

Collecting residuals and other information

add residuals and other information

STEP 4: Visualize the error around fit

# plot of data with mean and colored by residuals

STEP 3: Visualize the error around the null (mean weight)

Plot the fit error and the null error as 2 panels

Calculate \(R^2\)

\(R^2 = 1 - \displaystyle \frac {SS_{fit}}{SS_{null}}\)

check agains Rsq in your fit

Compare to traditional t-test

Provide your interpreation of the result