Module 9 Lab
Sara Coyne
2025-03-11
Loading Packages
library(tidymodels)## Warning: package 'tidymodels' was built under R version 4.4.3## ── Attaching packages ────────────────────────────────────── tidymodels 1.3.0 ──## ✔ broom 1.0.7 ✔ recipes 1.1.1
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(readr)
boston <- read_csv("boston.csv")## Rows: 506 Columns: 16
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (16): lon, lat, cmedv, crim, zn, indus, chas, nox, rm, age, dis, rad, ta...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.View(boston)Question 2
set.seed(123)
split <- initial_split(boston, prop = 0.7, strata = cmedv)
train <- training(split)
test <- testing(split)Quesion 3
cor(train) %>%
as_tibble(rownames = 'predictor_vars') %>%
select(predictor_vars, cmedv) %>%
arrange(desc(cmedv))## # A tibble: 16 × 2
## predictor_vars cmedv
## <chr> <dbl>
## 1 cmedv 1
## 2 rm 0.708
## 3 b 0.358
## 4 zn 0.344
## 5 dis 0.271
## 6 chas 0.165
## 7 lat -0.00202
## 8 lon -0.315
## 9 crim -0.384
## 10 rad -0.397
## 11 age -0.399
## 12 nox -0.439
## 13 tax -0.479
## 14 indus -0.490
## 15 ptratio -0.501
## 16 lstat -0.743The Variable with the strongest positive correlation is rm, and the one with the strongest negative correlation is lstat
Question 4
ggplot(train, aes(x = rm, y = cmedv)) +
geom_point(alpha = 0.2) +
geom_smooth(method = 'lm', se = FALSE)## `geom_smooth()` using formula = 'y ~ x'
Yes, this line is a pretty good representation of the relationship.
Question 5
boston_lm <- linear_reg() %>%
fit(cmedv ~ rm, data = train)
tidy(boston_lm)## # A tibble: 2 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -35.4 3.11 -11.4 8.70e-26
## 2 rm 9.22 0.491 18.8 7.46e-55Our model predicts that a house with 0 rm would sell for -$35,429. As the number of rooms in a hosue increases by 1, our model predicts the selling price would increase by $9,217. Both are statistically different than 0 based on their low p-values and their confidence intervals not including 0.
confint(boston_lm$fit)## 2.5 % 97.5 %
## (Intercept) -41.546106 -29.31285
## rm 8.250909 10.18311Question 6
boston_lm %>%
predict(test) %>%
bind_cols(test %>% select(cmedv)) %>%
rmse(truth = cmedv, estimate = .pred)## # A tibble: 1 × 3
## .metric .estimator .estimate
## <chr> <chr> <dbl>
## 1 rmse standard 6.83Question 7
boston_all <- linear_reg() %>%
fit(cmedv ~., data = train)
tidy(boston_all)## # A tibble: 16 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -608. 342. -1.78 7.64e- 2
## 2 lon -5.65 3.86 -1.46 1.45e- 1
## 3 lat 5.54 4.24 1.31 1.93e- 1
## 4 crim -0.0830 0.0396 -2.10 3.65e- 2
## 5 zn 0.0332 0.0165 2.01 4.56e- 2
## 6 indus -0.0143 0.0738 -0.193 8.47e- 1
## 7 chas 2.28 1.05 2.17 3.06e- 2
## 8 nox -11.7 4.74 -2.46 1.44e- 2
## 9 rm 4.37 0.516 8.46 8.13e-16
## 10 age -0.00921 0.0156 -0.591 5.55e- 1
## 11 dis -1.26 0.244 -5.17 4.06e- 7
## 12 rad 0.272 0.0790 3.44 6.47e- 4
## 13 tax -0.0121 0.00436 -2.78 5.78e- 3
## 14 ptratio -0.874 0.163 -5.37 1.48e- 7
## 15 b 0.0123 0.00310 3.97 8.72e- 5
## 16 lstat -0.479 0.0637 -7.51 5.24e-13The predictor variables that are statistically different than zero at the p value < 0.05 level are rm, dis, rad, tax, ptratio, b, and lstat. As the percentage of lower-status individuals increases by 1%, the selling price decreases by $478.60.
Question 8
boston_all %>%
predict(test) %>%
bind_cols(test %>% select(cmedv)) %>%
rmse(truth = cmedv, estimate = .pred)## # A tibble: 1 × 3
## .metric .estimator .estimate
## <chr> <chr> <dbl>
## 1 rmse standard 4.83On average, our linear regression is mispredicitng by ~$4,829. This is better than the model used for the rm predictor variable because the value is smaller.
Question 9
top_5 <- tidy(boston_all) %>%
filter(term != "(Intercept)") %>%
arrange(desc(statistic))
top_5## # A tibble: 15 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 rm 4.37 0.516 8.46 8.13e-16
## 2 b 0.0123 0.00310 3.97 8.72e- 5
## 3 rad 0.272 0.0790 3.44 6.47e- 4
## 4 chas 2.28 1.05 2.17 3.06e- 2
## 5 zn 0.0332 0.0165 2.01 4.56e- 2
## 6 lat 5.54 4.24 1.31 1.93e- 1
## 7 indus -0.0143 0.0738 -0.193 8.47e- 1
## 8 age -0.00921 0.0156 -0.591 5.55e- 1
## 9 lon -5.65 3.86 -1.46 1.45e- 1
## 10 crim -0.0830 0.0396 -2.10 3.65e- 2
## 11 nox -11.7 4.74 -2.46 1.44e- 2
## 12 tax -0.0121 0.00436 -2.78 5.78e- 3
## 13 dis -1.26 0.244 -5.17 4.06e- 7
## 14 ptratio -0.874 0.163 -5.37 1.48e- 7
## 15 lstat -0.479 0.0637 -7.51 5.24e-13The top 5 most influential predictor variables are rm, b, rad, chas, and zn.