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.
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