Homework 2

Due: October 24 at noon turn in the .html file on Sakai

Create a project called Homework 2 on Rstudio.cloud

The Diamonds data set can be used to examine the relationship between a diamond’s characteristics and it’s price. Using the Diamonds data set in the Stat2Data package, we want to assess following models:

(#1) TotalPrice = \(\beta_0 + \beta_1\)Depth + \(\beta_2\)Depth\(^2 + \epsilon\)

(#2) TotalPrice = \(\beta_0 + \beta_1\)Carat + \(\beta_2\)Depth\(+ \epsilon\)

(#3) TotalPrice = \(\beta_0 + \beta_1\)Carat + \(\beta_2\)Depth + \(\beta_3\)Depth\(\times\)Carat\(+ \epsilon\)

Inference

  1. Fit the three models. For each model (1, 2, and 3), report the \(\hat\beta\) values and confidence intervals. Interpret all \(\hat\beta\) coefficients in the context of the model fit.

Prediction

  1. Following the steps outlined when we discussed how to conduct a data analysis, create a report discussing the three models above. Use \(R^2\) and adjusted \(R^2\) to select your final prediction model. Be sure to follow all of the steps outlined, including testing the assumptions of each model and including the proper plots to demonstrate that the assumptions have been met.
  1. For the analysis in Exercise 2, rank each of the following principles from the Elements and Principles of Data Analysis article for this data analysis from 1 to 10 along with a one sentence summary: