This exercise involves the Boston housing data set.
(a) To begin, load in the Boston data set. The Boston data set is
part of the `ISLR2` library. 
Now the data set is contained in the object Boston.

Read about the data set:

### p_01

```{r boston_data}
library(ISLR2)
library(tidyverse)
library(MASS)

data("Boston")
#?Boston
```

### p_0b

How many rows are in this data set? How many columns? What
do the rows and columns represent?

```{r}
dim(Boston)
glimpse(Boston)
```

### p_1b  
Make some pairwise scatterplots of the predictors (columns) in this data set. Describe your findings.




```{r}
pairs(Boston)

```

Also have correlation matrix in heatmap with labels

```{r}
cor(Boston)
cor(Boston) %>% 
  corrplot::corrplot()
```
Have correlation between crim with other variables

```{r}
# Assuming Boston dataset is loaded and available
# Calculate the correlation matrix
cor_matrix <- cor(Boston)

# Extract the correlation of 'crim' with all other variables
crim_correlations <- cor_matrix["crim", ]

# Sort the correlations in descending order
sorted_crim_correlations <- sort(crim_correlations, decreasing = TRUE)

# Display the sorted correlations
print(sorted_crim_correlations)

```



### p_0c 
Are any of the predictors associated with per capita crime rate?   If so, explain the relationship. 



### p_0d 
Do any of the census tracts of Boston appear to have particularly high crime rates? Tax rates? Pupil-teacher ratios? Comment on the range of each predictor. 

```{r}
Boston %>% 
  dplyr::select(crim, tax, ptratio) %>% 
  summary()
``` 


```{r}
library(tidyverse)

# Assuming the Boston dataset is available
# Summarize the range and identify high values for 'crim', 'tax', and 'ptratio'
summary_stats <- Boston %>%
  summarise(
    crim_min = min(crim),
    crim_max = max(crim),
    tax_min = min(tax),
    tax_max = max(tax),
    ptratio_min = min(ptratio),
    ptratio_max = max(ptratio)
  )

# Identify high values based on chosen thresholds (e.g., top 5% as high)
high_values <- Boston %>%
  summarise(
    high_crim = quantile(crim, 0.95),
    high_tax = quantile(tax, 0.95),
    high_ptratio = quantile(ptratio, 0.95)
  ) %>%
  pivot_longer(cols = everything(), names_to = "variable", values_to = "threshold")

# Find the census tracts with particularly high values
high_tracts <- Boston %>%
  filter(
    crim > high_values$threshold[high_values$variable == "high_crim"] |
    tax > high_values$threshold[high_values$variable == "high_tax"] |
    ptratio > high_values$threshold[high_values$variable == "high_ptratio"]
  ) %>%
  dplyr::select(crim, tax, ptratio)

# Print the range of each predictor
print("Summary of Ranges:")
print(summary_stats)

# Print the high value thresholds for each variable
print("Thresholds for High Values (Top 5%):")
print(high_values)

# Display census tracts with high values
print("Census Tracts with High Values for 'crim', 'tax', or 'ptratio':")
print(head(high_tracts))

```


### p_0e 
How many of the 
census tracts in this data set bound the Charles river?


```{r}
Boston %>%
  filter(chas == 1) %>%
  nrow()
```
### p_0f
What is the median pupil-teacher ratio among the towns in this data set? 

```{r}
Boston %>%
  summarise(median_ptratio = median(ptratio))
```

### p_0g
Which census tract of Boston has lowest median value of owner occupied homes? What are the values of the other predictors for that census tract, and how do those values compare to the overall ranges for those predictors? Comment on your findings. 

```{r}
# Find the census tract with the lowest median value of owner-occupied homes
lowest_medv_tract <- Boston %>%
  filter(medv == min(medv)) %>%
  dplyr::select(everything())

# Summarize the range of each predictor in the dataset
overall_ranges <- Boston %>%
  summarise(across(everything(), list(min = min, max = max)))

# Display the census tract with the lowest 'medv'
print("Census Tract with the Lowest Median Value of Owner-Occupied Homes:")
print(lowest_medv_tract)

# Display the overall ranges for comparison
print("Overall Ranges for Each Predictor:")
print(overall_ranges)
```



### p_0h
In this data set, how many of the census tracts average more than seven rooms per dwelling? More than eight rooms per dwelling?   Comment on the census tracts that average more than eight rooms per dwelling. 

```{r}

# Count the number of census tracts with more than 7 rooms per dwelling
count_more_than_7 <- Boston %>%
  filter(rm > 7) %>%
  summarise(count = n())

# Count the number of census tracts with more than 8 rooms per dwelling
count_more_than_8 <- Boston %>%
  filter(rm > 8) %>%
  summarise(count = n())

# Display the results
print("Number of census tracts averaging more than 7 rooms per dwelling:")
print(count_more_than_7)

print("Number of census tracts averaging more than 8 rooms per dwelling:")
print(count_more_than_8)

# Display details of census tracts with more than 8 rooms per dwelling
tracts_more_than_8 <- Boston %>%
  filter(rm > 8) %>%
  dplyr::select(everything())

print("Details of census tracts averaging more than 8 rooms per dwelling:")
print(tracts_more_than_8)
```