Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Homework 1

See general homework tips and submit your files via the course website.

Setup code for the data set is provided in the HW1Data.sas file in the Homework 1 folder on the course website. The data set is based on the Glass Identification data from the UCI Machine Learning Repository. The original data and variables are described on http://archive.ics.uci.edu/ml/datasets/Glass+Identification. The original glass.data file is also available in the Homework 1 directory on CANVAS. The glassid data set for the homework omits the id number and several of the elements, and the Type of glass variable is replaced by a groupedtype variable which merges several combinations of glass types.

Exercise 1

Consider the refractive indices (RI) for glassware glass and headlamps glass.

a) Provide descriptive measures and plots for the refractive index for those two types of glass separately. Comment on similarities and differences in the location, spread, skew, and normality of each of the two samples.

b) For each of the two types of glass, perform a hypothesis test for whether the true location (mean or median) of the refractive index is significantly different from 1.52.  Whether you use mean or median will depend on which test is appropriate. State your conclusions for each of the types of glass. Be sure to consider the tests for part (a) when choosing your location tests in part b).

Exercise 2

Now we want to consider sodium (Na) content as a possible differentiator for glass from glassware and headlamps.

a) Comment on the typical amount of sodium in glassware and headlamps, and test and state your conclusions about normality of sodium content for each of these two types of glass.

b) Perform a hypothesis test of whether headlamps tend to have significantly higher amounts of sodium than glassware do and state your conclusion. Would higher levels of sodium in glass pieces from a sample suggest the glass is more likely from glassware or from a headlamp?

Exercise 3

We also want to consider relationships between refractive index and chemical content for glass from glassware and headlamps.

a) Obtain the Pearson correlation matrix for the numeric variables in the data set for glassware and headlamps combined. Comment on significant correlations and state what this tells us about the relationships between the glass attributes, and what we might infer about the population of glassware and headlamp glass based on this sample.

b) Perform the same correlation analysis for each of the two glass types separately. Comment on how the relationships between glass attributes differ between the two types of glass and note any differences with what you found in part (a).