Quantitative Analysis Exam

Quantitative Analysis Exam

 

Contents

 

1.  Introduction                    2
2.  Answer to Question 1                 3
3.  Answer to Question 2                 5
4.  Answer to Question 3                 6
5.  Answer to Question 4                 8
6.  Answer to Question 5                 10
7.  Answer to Question 6                 11
8.  Answer to Question 7                 12
9.  Answer to Question 8                 14
10. Answer to Question 9                 16
11. Marking Scheme and Comments              19

 

 

 

 

 

 

1. Introduction

 

Quantitative Analysis is a vital part of any problem solving, be it from Engineering, Economics,

Logistics  or  Business  Analysis.  It  enables  us  to  glean  information  from  statistical  and  other

analytical methods by which we can deduce much information that are otherwise not easily seen.

In business analysis, it is vital to extract information about correlation of data, i.e, whether the

sales quantities are related to weather, marketing poll results, changes in the economic landscape

or even changes in the political arena. To this end, it is necessary to perform regression analysis

before we can proceed any further. This assignment is focused on this area of data analysis/

The following sections comprise the answers to this assignment. This is a part of assignments for

Cohort No. 10.

 

 

The following is the data table that is referred to in the ensuing answers.

 

Machine  Age

Fuel

Consumption

Number  (Years)  (Ltr)

1  2  22

2  7.4  61

3  5.3  42

4  18  222

5  11.5  110

6  6.4  51

7  14.3  153

8  10.2  93

9  21  288

10  3.4  30

11  2.9  26

12  9.3  81

13  13.7  143

14  16.2  187

15  4.6  37

 

 

1.  Plot the data on graph paper, consider age of machine as “X” and fuel consumption as “Y”

 

The plot is shown in the next page.

 

 

 

 

 

 

2.  Calculate the correlation coefficient between “x” and “y”.

 

r  =   ……………(1)

 

 

 

 

We refer the following table for this calculation:

Machine  Age-x

Fuel Consumption-

y

 

Number  (Years)  (Ltr)  xy  x  y  x

2

y

2

 

1  2  22  44  2  22  4  484

2  7.4  61  451.4  7.4  61  54.76  3721

3  5.3  42  222.6  5.3  42  28.09  1764

4  18  222  3996  18  222  324  49284

5  11.5  110  1265  11.5  110  132.25  12100

6  6.4  51  326.4  6.4  51  40.96  2601

7  14.3  153  2187.9  14.3  153  204.49  23409

8  10.2  93  948.6  10.2  93  104.04  8649

9  21  288  6048  21  288  441  82944

10  3.4  30  102  3.4  30  11.56  900

11  2.9  26  75.4  2.9  26  8.41  676

12  9.3  81  753.3  9.3  81  86.49  6561

13  13.7  143  1959.1  13.7  143  187.69  20449

14  16.2  187  3029.4  16.2  187  262.44  34969

15  4.6  37  170.2  4.6  37  21.16  1369

 

 

 

 

 

 

 

3.  Construct the regression equation of the from     y =a +bx

 

 

 

 

 

 

 

 

 

 

 

 

 

Consider the following table values for this calculation:

 

Machine  Age-x

Fuel

Cons.-y

_  _

Number  (Years)  (Ltr)  x  y  xy  x  y  x

2

y

2

 

1  2  22  2  22  44  2  22  4  484

2  7.4  61  7.4  61  451.4  7.4  61  54.76  3721

3  5.3  42  5.3  42  222.6  5.3  42  28.09  1764

4  18  222  18  222  3996  18  222  324  49284

5  11.5  110  11.5  110  1265  11.5  110  132.25  12100

6  6.4  51  6.4  51  326.4  6.4  51  40.96  2601

7  14.3  153  14.3  153  2187.9  14.3  153  204.49  23409

8  10.2  93  10.2  93  948.6  10.2  93  104.04  8649

9  21  288  21  288  6048  21  288  441  82944

10  3.4  30  3.4  30  102  3.4  30  11.56  900

11  2.9  26  2.9  26  75.4  2.9  26  8.41  676

12  9.3  81  9.3  81  753.3  9.3  81  86.49  6561

13  13.7  143  13.7  143  1959.1  13.7  143  187.69  20449

14  16.2  187  16.2  187  3029.4  16.2  187  262.44  34969

15  4.6  37  4.6  37  170.2  4.6  37  21.16  1369

 

_  _

 

 

x  y

∑ xy  ∑ x ∑ y  ∑ x

2

∑ y

2

 

 

 

 

 

4.   Draw the regression line on the same graph

 

 

 

 

5.  Calculate R2 – value that measures the goodness of fit.

 

 

 

 

6.  In respect of each of the observations on age calculate the residual.

 

 

 

7.  a)   Calculate the mean of the residuals.
8. b)  Draw histogram of the residuals and comment on the results (use three class intervals)

 

 

 

8.  Draw another graph with “x” as machine number and “y” as residual and comment on the

result.

 

 

 

 

9.  Calculate the correlation coefficient between “x” (value of age) and residual and comment

on the result.

 

 

10.  Marking Scheme and Comments