Diamonds

library(tidyverse)
library(Stat2Data)
library(broom)

data("Diamonds")

What are the variable types in this dataset?

glimpse(Diamonds)

## Observations: 351
## Variables: 6
## $ Carat      <dbl> 1.08, 0.31, 0.31, 0.32, 0.33, 0.33, 0.35, 0.35, 0.37,…
## $ Color      <fct> E, F, H, F, D, G, F, F, F, D, E, F, D, D, F, F, D, D,…
## $ Clarity    <fct> VS1, VVS1, VS1, VVS1, IF, VVS1, VS1, VS1, VVS1, IF, V…
## $ Depth      <dbl> 68.6, 61.9, 62.1, 60.8, 60.8, 61.5, 62.5, 62.3, 61.4,…
## $ PricePerCt <dbl> 6693.3, 3159.0, 1755.0, 3159.0, 4758.8, 2895.8, 2457.…
## $ TotalPrice <dbl> 7228.8, 979.3, 544.1, 1010.9, 1570.4, 955.6, 860.0, 8…

What are the levels of the “Clarity” variable in the Diamonds data?

levels(Diamonds$Clarity)

## [1] "IF"   "SI1"  "SI2"  "SI3"  "VS1"  "VS2"  "VVS1" "VVS2"

Fit a model with TotalPrice as the outcome and Clarity as the explanatory variable

lm(TotalPrice ~ Clarity, data = Diamonds)

## 
## Call:
## lm(formula = TotalPrice ~ Clarity, data = Diamonds)
## 
## Coefficients:
## (Intercept)   ClaritySI1   ClaritySI2   ClaritySI3   ClarityVS1  
##     6396.56       -18.42       230.47     -2824.46      1234.23  
##  ClarityVS2  ClarityVVS1  ClarityVVS2  
##     1197.50      2279.81      1171.77

Change the referent category to “SI1” and refit the model

Diamonds <- Diamonds %>%
  mutate(
    Clarity = fct_relevel(Clarity, c("SI1", "IF", "SI2", "SI3", "VS1", "VS2", "VVS1", "VVS2"))
  )

levels(Diamonds$Clarity)

## [1] "SI1"  "IF"   "SI2"  "SI3"  "VS1"  "VS2"  "VVS1" "VVS2"

lm(TotalPrice ~ Clarity, data = Diamonds)

## 
## Call:
## lm(formula = TotalPrice ~ Clarity, data = Diamonds)
## 
## Coefficients:
## (Intercept)    ClarityIF   ClaritySI2   ClaritySI3   ClarityVS1  
##     6378.14        18.42       248.89     -2806.04      1252.65  
##  ClarityVS2  ClarityVVS1  ClarityVVS2  
##     1215.92      2298.23      1190.19

Add the variable “Depth” to your model. How do you interpret the coefficient for this parameter?

lm(TotalPrice ~ Clarity + Depth, data = Diamonds)

## 
## Call:
## lm(formula = TotalPrice ~ Clarity + Depth, data = Diamonds)
## 
## Coefficients:
## (Intercept)    ClarityIF   ClaritySI2   ClaritySI3   ClarityVS1  
##  -1.377e+04   -6.338e+02   -5.031e-01   -2.550e+03    6.044e+02  
##  ClarityVS2  ClarityVVS1  ClarityVVS2        Depth  
##   4.310e+02    1.280e+03    8.399e+02    3.221e+02

Fit a model with the outcome TotalPrice using Depth, Depth^2, and Color

lm(TotalPrice ~ Depth + I(Depth^2) + Color, data = Diamonds) %>%
  tidy(conf.int = TRUE)

## # A tibble: 9 x 7
##   term         estimate std.error statistic p.value  conf.low conf.high
##   <chr>           <dbl>     <dbl>     <dbl>   <dbl>     <dbl>     <dbl>
## 1 (Intercept) -49243.    109675.     -0.449  0.654  -264966.   166480. 
## 2 Depth         1393.      3279.      0.425  0.671    -5056.     7843. 
## 3 I(Depth^2)      -8.28      24.3    -0.341  0.734      -56.1      39.6
## 4 ColorE       -1415.      1319.     -1.07   0.284    -4009.     1179. 
## 5 ColorF        3082.      1306.      2.36   0.0189     512.     5651. 
## 6 ColorG        3394.      1313.      2.58   0.0102     811.     5977. 
## 7 ColorH        2511.      1726.      1.45   0.147     -884.     5906. 
## 8 ColorI        2480.      2377.      1.04   0.298    -2195.     7155. 
## 9 ColorJ       -3218.      4401.     -0.731  0.465   -11873.     5438.

Calculate the .25 and .75 quantiles of Depth

Diamonds %>%
  summarize(q_25 = quantile(Depth, 0.25),
            q_75 = quantile(Depth, 0.75))

##   q_25  q_75
## 1 61.2 68.55

1393.43 * (68.55 - 61.2) - 8.28 * (68.55 ^ 2 -61.2 ^ 2)

## [1] 2345.385

Interpret the effect of Depth and Color = E

The coefficient for the linear term for depth is 1393.43 (95% CI: -5056.41, 7843.27). The quandratic term for depth is -8.28 (95% CI: -56.12, 39.55). A interquartile range change (from 61.2 to 68.55) in depth yields an expected change in total price of 2345.39 holding Color constant.

The coefficient for when Color is E (compared to D) is -1415.17 (95% CI: 4008.92, 1178.58). A diamond that has Color E has an expected total price of 1415.17 less than one with Color D, holding depth constant.