## Data Analysis and Modelling

This is the question set Data Analysis and Modelling Spring 2015, which was taken by the Pokhara University.

**Pokhara University – Data Analysis and Modelling Spring 2015**

Level: Bachelor | Semester –Spring | Year: 2015 |

Program: BBA/BI/BCIS/BBA-TT | Full Marks: 100 | |

Course: Data Analysis and Modelling | Pass Marks: 45 | |

Time: 3hrs. |

Section “A”

**Very Short Answer Questions**

Attempt all the questions.

- What is the difference between correlation analysis and regression analysis?
- For a set of 8 data points, the sum of squared differences between observed and estimated values of Y is 35.72. Given this information, what is the standard error of estimate?
- With reference to the given multiple regression:

Interpret the meaning of slopes and coefficient of multiple

determination if R^{2 }= 0.90 - Given the following information from a simple regression analysis:

n=20, b_{1}=4, b_{2}=3, S_{b1}=1.2, S_{b2}=0.8, set up a 95% confidence interval estimate of the population slope**β**_{2}_{.} - Form the given information calculate the forecast for the year 2006 using Exponential smoothing constant 0.1 and forecast for the year 2003 was 195 units.

- What is the cost of living index number? What does it measure?
- Convert the following profit matrix into the opportunity loss matrix.

- Detect active and inactive constraints of following LPP.

Max Z=5x+7y

S.t

2x+3y 30

3x+5y 45

x 0,y 0

Where max z = 62 at x= 4 and y=6 - Write down the assumption of the linear regression model.
- Find the critical path and project duration (in weeks) from the following network diagram

Section “B”

**Descriptive Answer Questions**Attempt any

questions*six* - A firm administers a test to sales trainees before they go into the field. The management of the firm is interested in determining the relationship between the test scores and the sales made by the trainees at the end of one year in the field. The following data were collected for 10 sales personnel who have been in the field:

Calculation shows that

S*X* = 34 S*X*^{2} = 122.6

S*Y* = 1371 S*Y*^{2} = 201121

S*XY* = 4954

- Find the correlation coefficient between the test score and the number of units sold, examine if this linear relationship is significant at the 5% level of significance.
- Compute the 90% prediction interval for the Number of units sold of salesperson 9.
- Find the coefficient of determination and interpret its meaning.

12.The money Bank desires to open a new checking account for customers who will write at least 30 checks per month to assist in selecting new customers, the bank has studied the relationship between the number of checks written and the age and income of eight of their present customers. AGE was recorded to of nearest year and annual INCOME was recorded in thousand dollars. The data follow:

- Develop an estimating equation to use age and income to predict the number of checks written per month.
- Find the standard error of the estimate and interpret it.
- How many checks per month would be expected from a 35-year-old with an annual income of $22,500

13. The sales manager responsible for the appliance division of a large consumer products company has collected the following data regarding unit sales for his division during the last 5 years.

The equation describing the secular trend for appliance sales is

Where 1993 = 0 and x units = 1year

- Calculate the percent of trend and the relative cyclical residual of these data.
- In which year does the largest fluctuation from the trend occur? Is it the Same for both methods?
- Calculate MAPE for these data.

14.

- Use the following data to construct a cost living index number using the weighted arithmetic mean as the average.

- Write the dual of the following problem.

Maximize Z=

15. a) Consider the following time series data.

Use α=0.2 to compute the exponential smoothing forecast values for the time series. What is the forecast for week 7? Calculate MSE as well

b)Four jobs are to be done on four different machines. The cost ( in rupees ) of producing its job on the machine is given:

16.Yahoo trucking company has a contract to move 115 truckloads of sand per week between three sand-washing plants W, X, and Y, and the three destinations, A, B, and C. Cost and volume information is given below. Compute the starting solution by Vogel’s approximation method and then find an optimal solution by using MODI Method.

17.A small project composed of eight activities and their time estimates are as follows:

Section “C”

**Case Analysis**

18.a) Successful selling is as much an art as a science, but many sales managers believe that personal attributes are important in predicting sales success. Design Alley is a full-service interior design store that sells custom blinds, carpets, and wall coverings. The store manager, Mr. Adhikari, contracted with a sales- force selection company to conduct a pre-hiring tests on four aptitudes. Mr. Adhikari has collected sales growth data for 25 of the salespeople who were hired, along with the scores from the four tests of aptitude: **creativity**, **mechanical ability**, **abstract thinking**, and **mathematical calculation**. Mr. Adhikari generated the following Minitab output.

b) You are the manager of a small store that specializes in hats, sunglasses, and other accessories. You are considering a sales promotion of a new line of hats and sunglasses. You will offer the sunglasses only to those who purchase two or more hats, so you will sell at least twice as many hats as pairs of sunglasses. Moreover, your supplier tells you that, due to seasonal demand, your order of sunglasses cannot exceed 100 pairs. To ensure that the sale items fill out the large display you have set aside, you estimate that you should order at least 210 items in all.

- Assume that you will lose $3 on every hat and $2 on every pair of sunglasses sold. Given the constraints above, how many hats and pairs of sunglasses should you order to lose the least amount of money in the sales promotion?
- Suppose instead that you lose $1 on every hat sold but make a profit of $5 on every pair of sunglasses sold. How many hats and pairs of sunglasses should you order to make the largest profit in the sales promotion?

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