## Data Analysis and Modeling – Fall, 2015

This is the question set along with answers Data Analysis and Modeling Fall 2015, which was taken by the Pokhara University.

**Pokhara University – Data Analysis and Modeling Fall 2015**

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

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

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

Time: 3hrs. |

Attempt all the questions.

- The vice president for research and development of a large chemical and manufacturing company believes that the firm’s annual profit depends on the amount spent on research and development (R&D). The new chief executive officer does not agree and has asked for evidence. Here are the data for six years.

a) Find the correlation coefficient between annual profit and money spent on research and development. What type of relationship is existing between these two variables? Comment on your result.

b) Develop the estimation equation that best fits the data. Predict annual profit when the amount spent on research and development is 10 million. Does this model is appropriate for the prediction of annual profit when three is 25 million spent on research and development? Explain.

c) Calculate the sample coefficient determinate. Does the regression equation development in part (b) is appropriate for predictive purposes or the student should search elsewhere for additional explanatory variables? Explain. - A statistics professor in a leading business school has a keen interest in factors affecting students’ performance on exams. The midterm exam for the past semester had a wide distribution of grades but he feels certain several factors explain the distribution. He allowed his student to study the varying amounts of time for exams to develop a predicting formula for exam grades, he asked his 15 students at random and processed these data using Microsoft Excel to obtain the following results.

**Required:**a) Determinate the regression equation. How much grade will be obtained by a student who is 22 years now reads 5 different books related to a subject 4 hours a day and has an IQ score7?

b) Which of the given independent variables are batter explanatory variables to measure the grade point? State explicit hypotheses test them at 0.10 level of signification and state an explicit conclusion.

c) What proportion of variation in grade point is explained by four independent variables? What conclusion does this result reflect about the appropriateness of the model?

d) Final standard error of overall regression model and interpret its meaning.

e) Test at 0.01 level of significance, the overall fit of the model. Is your fitted regression model is significant as a whole? Use the p-value approach in making your decisions. - The sales manager responsible for the application 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 application sales is

Y=52.4+9.2X Where 1993 = 0 and x unit = 1 year

a) Calculate the percent of the trend for these data.

b) Calculate the relative cyclical residual for these data.

c) In which year does the largest fluctuation from trend occur and is it the same for both methods?

d) Forecast the sales units for the year 1999and measure their accuracy by MSE. - a) The capacity of the wai wai production line is 75 lots per day. The capacity of the GolMol line is 50 lots per day. In department A, WaiWai requires 2 labor hours and the GolMol requires 3 labor hours; presently in department A; a maximum of 90 labor hours per day can be assigned to the production of the two types of noodle. In department B, the waiwai requires 3 labor hours and Golmol also requires 4 labor hours. Presently in department B, a maximum of 120 labor hours per day can be assigned to the production of the two types of noodles. The profit contributions are 23 and 12 respectively, for each WaiWai and GolMol lot. Then formulate and solve graphically the linear programming model.

b) Write the dual of the following problem.

Maximize z=5×1+4×2-2×3

subject to the constraints:

2×1 -3×2 +8×3 ≤10

-4×1 +2×2 -2×3 ≤12

3×1 -8×2 +x3=1

x1≥0,×2≥ 0, x3unrestricted. - a) Everest Construction Company moves material between three plants and project A requires 35 units of material each project B requires 45 units and project C requires35 units .plant X can supply 55 units, plant Ycan supply 25 units, and plant Z can supply 35 units Using the following cost information, obtain the optimum transportation cost.

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

What is the job assignment which will minimize cost? - a) A research firm is planning a questionnaire survey on sexual harassment to office lady; The following are the activities to be carried out for the survey

i. What are the expected task durations and the variance of task duration.

ii. Draw a network for the project and find the critical path. What is the expected duration of the project?

iii. What is the probability that the project will not exceed 60 days?

b) The executive Council of Pokhara University wants to keep track of the budget that each engineering department requires to recruit new graduate student .the council has received the following data from four departments

Calculate an unweighted average of the relative index for the year 2011 and 2012 using 2010 as the base year - Write short notes on any two:

a) Multicollinearity.

b) Differentiate between the primal and dual problems of linear programming.

c) Use of CPM for project evaluation.

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