Add HW4 and HW5

HW5.Rmd

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+---
+title: "Assignment 3"
+subtitle: "STAT3373"
+author: "Isaac Shoebottom"
+date: "Oct 16th, 2025"
+output:
+  pdf_document: default
+  html_document:
+    df_print: paged
+---
+
+```{r message=FALSE, warning=FALSE}
+library(tidyverse)
+```
+
+# Question 1
+
+## a)
+
+```{r}
+latin_data <- tribble(
+  ~sunlight,      ~soil,   ~treatment, ~growth,
+  "Sunny",        "Sandy", "C", 45,
+  "Sunny",        "Loamy", "A", 52,
+  "Sunny",        "Clay",  "B", 48,
+  "Sunny",        "Sandy", "B", 43,
+  "Sunny",        "Loamy", "C", 50,
+  "Sunny",        "Clay",  "A", 49,
+  "Sunny",        "Sandy", "A", 47,
+  "Sunny",        "Loamy", "B", 51,
+  "Sunny",        "Clay",  "C", 46,
+  
+  "Partial Sun",  "Sandy", "A", 41,
+  "Partial Sun",  "Loamy", "B", 44,
+  "Partial Sun",  "Clay",  "C", 38,
+  "Partial Sun",  "Sandy", "B", 39,
+  "Partial Sun",  "Loamy", "C", 42,
+  "Partial Sun",  "Clay",  "A", 40,
+  "Partial Sun",  "Sandy", "C", 40,
+  "Partial Sun",  "Loamy", "A", 43,
+  "Partial Sun",  "Clay",  "B", 41,
+  
+  "Shade",        "Sandy", "B", 32,
+  "Shade",        "Loamy", "C", 35,
+  "Shade",        "Clay",  "A", 33,
+  "Shade",        "Sandy", "C", 31,
+  "Shade",        "Loamy", "A", 36,
+  "Shade",        "Clay",  "B", 34,
+  "Shade",        "Sandy", "A", 30,
+  "Shade",        "Loamy", "B", 33,
+  "Shade",        "Clay",  "C", 32
+)
+
+latin_data
+```
+
+## b)
+
+
+```{r}
+treatment_means <- latin_data %>%
+  group_by(treatment) %>%
+  summarise(mean_growth = mean(growth))
+
+treatment_means
+```
+
+## c)
+
+Mean Growth by Sunlight Level
+```{r}
+sunlight_means <- latin_data %>%
+  group_by(sunlight) %>%
+  summarise(mean_growth = mean(growth))
+
+sunlight_means
+```
+
+Mean Growth by Soil Type
+```{r}
+soil_means <- latin_data %>%
+  group_by(soil) %>%
+  summarise(mean_growth = mean(growth))
+
+soil_means
+```
+
+## d)
+
+From the descriptive statistics:
+
+Sunlight effects: Growth is highest under Sunny, moderate under Partial Sun, and lowest under Shade. This suggests sunlight has a strong positive effect on growth.
+
+Soil effects: Loamy soil consistently produces higher growth than Sandy or Clay, indicating soil type is an important blocking factor.
+
+Treatment effects: If the treatment means differ noticeably:
+
+- The watering schedule with the highest mean appears most effective.
+
+- Smaller differences suggest weaker treatment effects relative to blocking factors.
+
+- Because the Latin square controls for sunlight and soil, observed treatment differences are less confounded.
+
+## e)
+A Latin square ANOVA partitions variation into:
+
+- Sunlight (row effect)
+
+- Soil type (column effect)
+
+- Treatment effect
+
+- Error
+
+Expected Findings:
+
+- Sunlight effect: Likely highly significant, given the strong gradient from Sunny to Shade.
+
+- Soil effect: Likely significant, especially if Loamy soil dominates.
+
+- Treatment effect:
+
+	- Possibly significant if Daily watering shows consistently higher growth.
+
+	- Could be marginal if differences among watering schedules are small compared to sunlight and soil.
+
+- Error variance: Expected to be relatively small due to strong blocking.