Reference no: EM132760708
BUS 306 Quantitative Business Analysis - Emirates College of Technology
Problem Solving 1:
In order to monitor and improve it productivity, a company made an investigation and found out that the factors that affect the productivity the most are the absenteeism and the training sessions. The company data analytics department have collected data about the three variables (Productivity, Absenteeism, and Training Sessions) for the 12 past years as shown in the table below. Now the purpose of the company is to determine, through regression analysis, which of the two factors affects the productivity the most, then use that factor to forecast future productivities.
|
Year
|
Absenteeism
(in number of absent worker)
|
Training sessions
(in number of training Days)
|
Productivity
(in Million AED)
|
|
1
|
20
|
44
|
308
|
|
2
|
35
|
72
|
267
|
|
3
|
15
|
50
|
330
|
|
4
|
20
|
88
|
341
|
|
5
|
42
|
28
|
213
|
|
6
|
52
|
19
|
164
|
|
7
|
74
|
49
|
98
|
|
8
|
48
|
76
|
217
|
|
9
|
37
|
65
|
254
|
|
10
|
11
|
32
|
340
|
|
11
|
18
|
44
|
314
|
|
12
|
63
|
38
|
129
|
Questions:
1. Construct a scatter diagram for the data about productivity and absenteeism then interpret the possible relationship that can be found.
2. Construct a scatter diagram for the data about productivity and training sessions then interpret the possible relationship that can be found.
3. Construct a simple regression model to predict the annualproductivity by the variable Absenteeism. What is the interpretation that can be made based on the regression results?
4. Construct a simple regression model to predict the annual productivity by the variable Training Sessions. What is the interpretation that can be made based on the regression results?
5. Find r2 for the two regression models constructed earlier. Which factor explains the variable Productivity the most?
6. Calculate the prediction error for the annual productivity when the absenteeism value is equal to 11 and 63days, based on the corresponding regression model constructed previously.
7. For the regression model of the annualproductivity by the variable Absenteeism, draw the errors graph and check if the model respects the regression assumptions or not.
8. For the regression model of the annualproductivity by thevariable Training sessions, construct the ANOVA table for the regression model. Then perform the significance test for α = 0.05 and what conclusion can be drawn from the obtained results?
Problem Solving 2:
In the following table represents data on laptops sales for 7 periods.
|
Data on Laptops Sales
|
|
period
|
Sales of Laptops
|
|
1
|
670
|
|
2
|
750
|
|
3
|
620
|
|
4
|
520
|
|
5
|
410
|
|
6
|
500
|
|
7
|
590
|
|
8
|
None
|
Questions:
1. Compute The forecasting of the periods 5,6, and 8 using the Simple Moving Average of order 1, 3, and then 4.
2. Compute The forecasting of the periods 7, and 8 using the weighed moving average of order 2 (the weights are 15 and 5 from most recent period).
3. Compute The forecasting of the periods6, and 8 using the weighed moving average of order 4 (the weights are 12, 6, 7, and 4 from most recent period).
4. Compute the forecasting of period 7, for demand of computers, using the exponential smoothing with α = 0.4 and F4= 500.
Problem Solving 3:
We propose the following linear programming model.
Questions:
Use the graphical methods to find the optimal solution to the proposed linear program.
Max Z = 20.x1+ 80.x2
Subject to:
x1+3.x2 ≤ 90
x1+ x2 ≤ 40
4.x1+ x2 ≤ 120
x1, x2≥ 0
Attachment:- Quantitative Business Analysis.rar