Midterm Problem Solution

You can use Word, Excel, Power Point and R to answer the questions in this test.  There are a total of five (5) multi-part questions, with point values noted for each question. 

Please show your calculations, or the details of your program(s) for each problem. The R programs should be commented so that each step is clearly explained.

Combine all your answers/files  into a single zipped file and post the zipped  file to “Midterm” in CANVAS.

#1 (10 points)

For the experiment consisting of a single die toss, let

A = {outcome is <= 3}

B = {1,2,5,6}

C = {outcome is odd}

Please answer each of the following three True/False questions.  Show your work.

a).      True or False?

b).     True or False?
c).      True or False?

 

#2 (10 Points)

Is the following function a proper distance function?  Why?  Explain your answer.



Hint: Measure the distance between (0,0), (0,1) and (1,1)

 

#3 (20 points)

Using R perform the following

a)     Load the following CSV file to your R environment:       http://www.math.smith.edu/sasr/datasets/help.csv

b)     Create a dataframe of: id, age, “number of days any substance used” (daysanysub), substance, and race group

c)      Normalize “number of days any substance used” (daysanysub)

d)    Substitute the missing values of  “daysanysub” with zero

e)    Calculate: Mean, Max, Median, STD of Age

f)   Create a categorical variable “age_group” as:

                                               i.       From 0 up to and including 30        =”Young”

                                           ii.       Over 30 up to and including 60      =”Middle Age”

                                       iii.       Older than 60                                     =”OLD”

g)  Create “training” and “test” datasets by:

Choosing every third record as “test” and the remaining records as “training”.

 

#4 (20 Points)

A telecommunications company is concerned about the number of customers leaving their business (Chur=True). Using past data, an analyst has prepared the table below. Using the table below, calculate the following probabilities:

P(Churn=True)

P(Churn=False)

P(International Plan=Yes)

P(Voice Plan=Yes)

P(International Plan=Yes, Voice Plan=Yes)

Are “Voice Plan” and “International plan” independent?

P( (International Plan=Yes, Voice Plan=Yes)/Churn=True)

P( (International Plan=Yes, Voice Plan=Yes)/Churn=False)

P( Churn=False/(International Plan=Yes, Voice Plan=Yes ))

P( Churn=False/(International Plan=Yes, Voice Plan=Yes ))

 

#5  (40 Points)

a)     A telecommunications company is analyzing its customers’ data  for those customers that had between 0 and 175 “Day”, “Eve” and “Night” calls.  To estimate the missing “Night Calls”  field, the company is using k-nearest neighbors.

·        What would be the value of “Night Calls” for customer x in the table below if:

K = 1 and method = ”unweighted vote” is used

K = 2 and method = ”unweighted vote” is used

K = 3 and method = ”distance weighted vote” is used?

Customer     Day Calls      Eve Calls       Night Calls

A         110     99       91

B         123     103     103

C          71      88       89

D         113     122     121

E          98       101     118

X         114     110     ?

 

 

b)    The company has decided to classify “Night Calls” by category instead of estimating a number.  Furthermore, it has obtained additional customer information with the exact profile of customer X.

·        What would be the “Night Call” category for X if K=3 and distance weighted vote is used?  Why?