mardia_dm1633_assignment9.Rmd

---
title: "assignment9"
output:
  pdf_document: default
  html_document: default
date: "2023-04-14"
---
#HW09
#Use the R programs covered in the MultipleTesting module as a guide for HW09.

#Perform a multiple regression on all 100 predictors from the meatspec dataset in the 
#faraway package and extract the p-values for the coefficients of the 100 variables.


```{r}
library(faraway)
data(meatspec,package="faraway")  #the dataset meatspec is found in the faraway package

lmod=lm(fat ~ . , data=meatspec)
summary(lmod)  
# Extract p-values for coefficients and exluding the intercept
p_values <- summary(lmod)$coefficients[-1, 4]

```

```{r}
p_values
```
```{r}
#Use the p-values vector to list the variables with coefficients that are significantly
#different from 0 with  
#a) using no FWER adjustment (alpha=.05 for each test of hypothesis).
alpha <- 0.05
print(p_values[p_values < alpha])
names(p_values[p_values < alpha])

# We reject these 15 features based on the p values
```
```{r}
#b) using the Bonferroni procedure to control the FWER alpha at 0.05.
#Get adjusted p value
p_values_bonfadjust <- p.adjust(p_values, method = "bonferroni")

# Identify variables with significant coefficients
adj_bonferroni <- p_values_bonfadjust[p_values_bonfadjust < alpha]

adj_bonferroni
names(adj_bonferroni)

# We reject only V1 based on the Bonferroni procedure

```
```{r}

#c) using the Holm procedure to control the FWER alpha at 0.05.

# Get the adjusted p-val
p_values_holmadjust <- p.adjust(p_values, method = "holm")

# Identify variables with significant coefficients
adj_holm <- p_values_holmadjust[p_values_holmadjust < alpha]
adj_holm
names(adj_holm)

#We again reject only V1 based on Holm procedure as well

```