## Description

Submit two files through Blackboard: (a) .Rmd R Markdown file with answers and code

and (b) Word document of knitted R Markdown file. Your file should be named as follows:

“HW[X]-[Full Name]-[Class Time]” and include those details in the body of your file.

Complete your work individually and comment your code for full credit. For an example of

how to format your homework see the files posted with Lecture 1 on Blackboard. Show all

of your code in the knitted Word document.

1. Read the posted article, “Bordeaux wine vintage quality and weather,” by Ashenfelter,

Ashmore, and LaLonde (CHANCE, 1995). Three regression models are considered in

this article. Answer the following questions:

(a) What is a wine “vintage”?

(b) What is the response variable for the three models described in this paper?

Now, download the data in “wine.txt”. This is some of the data the authors used

to fit their models. The columns are: vintage (VINT), log of average vintage price

relative to 1961 (LPRICE2), rainfall in the months preceding the vintage in mL

(WRAIN), average temperature over the growing season in ◦C (DEGREES), rainfall in September and August in mL (HRAIN), and age of wine in years (TIME SV).

Note: the average temperature in September is not available in our data set so we

cannot fit the third regression model from the paper.

(c) Which values of LPRICE2 are missing and, according to the article, why have they

been omitted?

(d) Make a scatterplot matrix of the variables (explanatory and response) included in

the models. Describe what you see.

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(e) Fit the two regression models from the paper. Which is the best regression model?

Justify your answer and include relevant output (let α = 0.05). Did you choose the

same model as the authors?

(f) What is the sample size for your models?

(g) Write out the regression equation of the model you chose in part (e). Remember to

include the units of measurement. Interpret the partial slopes and the y-intercept.

Does the y-intercept have a practical interpretation?

(h) Make a table with the following statistics for both models: SSE, RMSE, PRESS,

and RMSEjackknife. Compare the relevant statistics. Based on this information,

would you change your answer to part (e)? Justify your answers.

(i) Could we use these regression models to predict quality for wines produced in 2005?

Justify your answer.

2. We will model the prestige level of occupations using variables such as education and

income levels. This data was collected in 1971 by Statistics Canada (the Canadian

equivalent of the U.S. Census Bureau or the National Bureau of Statistics of China)1

.

The data is in the file “prestige.dat” and the variables are described below:

variable description

prestige (y) Pineo-Porter prestige score for occupation, from a social survey

conducted in the mid-1960s

education average education of occupational incumbents, years, in 1971

income average income of incumbents, dollars, in 1971

women percentage of incumbents who are women

census Canadian Census occupational code

type type of occupation: “bc”=blue collar,

“prof”= professional/managerial/technical,

“wc”=white collar

(a) Do some internet research and write a short paragraph in your own words about

how the Pineo-Porter prestige score is computed. Include the reference(s) you used.

Do you think this score is a reliable measure? Justify your answer.

(b) Create a scatterplot matrix of all the quantitative variables. Use a different symbol

for each profession type: no type (pch=3), “bc” (pch=6), “prof” (pch=8), and “wc”

(pch=0) when making your plot. For the remainder of this question, we will use the

explanatory variables: income, education, and type. Does restricting our regression

to only these variables make sense given your exploratory analysis? Justify your

answer.

1Source: Canada (1971) Census of Canada. Vol. 3, Part 6. Statistics Canada; 19-1–19-21.

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(c) Which professions are missing “type”? Since the other variables for these observations are available, we could group them together as a fourth professional category

to include them in the analysis. Is this advisable or should we remove them from

our data set? Justify your answer.

(d) Visually, does there seem to be an interaction between type and education and/or

type and income? Justify your answer.

(e) Fit a model to predict prestige using: income, education, type, and any interaction

terms based on your answer to part (d). Evaluate the model and include relevant

output. Use your answer to part (c) to determine which observations to use in your

analysis.

(f) Create a histogram of income and a second histogram of log(income) (i.e., natural

logarithm). How does the distribution change?

(g) Fit the model in (e) but this time use log(income) (i.e., natural logarithm) instead

of income. Evaluate the model and provide the relevant output.

(h) Is the model in (e) or (g) better? Justify your answer. Why can’t we use a partial

F-test here?

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