Statistics Worksheet

Franklin UniversityMath 280 – Introduction to Probability and Statistics
Name: _____________________
Module 10 Application Assignment (16 Points)
The points on this assignment total up to 45 points. Your percent score from this assignment will be
multiplied by 16 to find your actual assignment grade (out of 16) for the gradebook.
PART I. PRICE ELASTICITY
You are a financial manager for an IT company specializing in uninterruptible power supplies (UPS) and
other battery / remote power solutions. Your area Vice President gives you the historical sales data
below and asks you to provide a sales forecast for the next four weeks for your company’s best-selling
UPS: the Convergys 2.0. [The data set is provided as an Excel file on the assignment page]
Convergys 2.0
Convergys 2.0
Fiscal
Week #
Price
($)
Units
Sold
Fiscal
Week #
Price
($)
Units
Sold
1
367
106
21
446
115
2
200
196
22
360
109
3
372
125
23
274
127
4
376
115
24
543
65
5
521
69
25
331
146
6
480
98
26
318
174
7
319
178
27
528
85
8
371
122
28
481
88
9
600
54
29
379
153
10
289
155
30
485
100
11
569
65
31
258
176
32
268
151
12
321
124
33
416
129
13
249
154
34
571
56
14
435
126
35
371
124
15
247
186
36
600
51
16
317
146
37
450
17
573
62
38
500
8
624
43
39
525
19
437
121
40
475
20
442
88
1
081020
Franklin University
Math 280 – Introduction to Probability and Statistics
Name: _____________________
1. (4 points) Create a scatterplot for Convergys 2.0, showing the relationship between price and units
sold. Be sure the independent and dependent variables are on the correct axes, and that your graph
looks professional and is labeled and titled appropriately. Paste your scatterplot below (you may
use either MS Excel or Jamovi).
2. (6 points) Perform a linear regression on Convergys 2.0’s units sold based on price. Below, write the
formula for units sold in terms of price, and provide the coefficient of determination and the
coefficient of correlation (make sure you label these and use the right symbols!).
3. (4 points) Use your answers from previous questions to predict the number of Convergys 2.0 units
that will be sold in weeks 37 through 40 (fill the values in to the table above on page one).
4. (3 points) If the price of the Convergys 2.0 increased by $100 from one week to the next, how would
you expect the number of units sold to change? Show your work.
5. (6 points) Calculate the residuals for Convergys 2.0’s units sold for weeks 1-36 (round all answers to
the nearest unit). Fill-in the residual frequency table below and also include a histogram of this
data. Based on this new information, do you still agree that linear regression was a good choice for
this analysis? Why? (Hint: how would you describe the shape of this distribution?)
Convergys 2.0
Residual Range
Frequency
< -40 -40 to -31 -30 to -21 -20 to -11 -10 to -1 0 to 9 10 to 19 20 to 29 30 to 39 40+ TOTAL (should be 36) 2 081020 Franklin University Math 280 – Introduction to Probability and Statistics Name: _____________________ PART II. DATA CENTER REDESIGN You are a data center manager and have been asked by your boss to redesign a telecommunications room in one of your smaller facilities. One element of this redesign you would like to optimize is the rack structure – your goal is to provide the greatest amount of equipment storage (by weight) within the cost constraints of the project. There are two types of storage racks you can choose from. Rack A costs $400 per unit, requires three square feet of floor space, and can support up to 80 pounds of equipment. Rack B costs $800 per unit, requires four square feet of floor space, and can support up to 120 pounds of equipment. Your budget for this aspect of the project is $5600, though of course you don’t have to spend all of it. Additionally, you can allocate at most 36 square feet of floor space to the racks in this room. How many of each type of rack should you buy in order to maximize the amount of equipment that could be supported? 1. (2 points) What are your variables for this project? Assign each a letter and describe them in words. 2. (2 points) What is the objective function you are being asked to maximize? Assign it a variable, define it in words, and provide an equation for it using the variables you defined above. 3. (6 points) There are four constraints for this problem (hint: one is for the cost of the racks, one is for floor space, and two other ‘natural’ constraints). Write these four constraints in equation form 4. (5 points) Using MS Word, MS Excel, Jamovi or a web-based graphing tool like www.fooplot.com, create a graph of these constraints. Your graph should include the equations of the constraints and indicate which area is the feasible region of possible solutions. 5. (4 points) Based on your graph, how many points are possible solutions? Give the coordinates of each of these points and evaluate the objective function at each point. 6. (3 points) Now we can answer our original problem: how many of each type of rack should you buy to maximize the amount of equipment that this room can support? Also, indicate how much of your original budget you will spend and the amount of floor space these racks will take up in total. 3 081020 Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Convergys 2.0 Price Units 367 106 200 196 372 125 376 115 521 69 480 98 319 178 371 122 600 54 289 155 569 65 321 124 249 154 435 126 247 186 317 146 573 62 624 43 437 121 442 88 446 115 360 109 274 127 543 65 331 146 318 174 528 85 481 88 379 153 485 100 258 176 268 151 416 129 571 56 371 124 600 51 450 500 525 475