# Data Analysis & Modeling || Spring, 2016 || Pokhara University || BBA/BCIS

## Data Analysis and Modeling – Spring, 2016

This is the question set along with answers Data Analysis and Modeling Spring 2016, which was taken by the Pokhara University.

Pokhara University – Data Analysis and Modeling Spring 2016

 Level:  Bachelor Semester –Spring Year: 2016 Program:BBA/BBA-BI/BBA-TT/BCIS Full Marks: 100 Course: Data Analysis and Modeling Pass Marks: 45 Time:  3hrs.

Section “A”

Attempt all the questions.

1. In a regression problem with a sample size of 25, the slope was found to be 1.12and the standard error of estimate 8.516. The quantity , where X is an independent variable. Find the standard error of the regression slope coefficient.
2. With reference to the given multiple regression:
ˆY = 96.458 +136.485X1 -2.403X2,
where, Y = rent of apartment(in Rs. per month)
X1 = size of apartment (number of rooms)
X2 = distance from downtown ( in miles)
Interpret the regression coefficients.
3. Reconstruct the following indices using 2005 as the base. 4. Define balanced and unbalanced assignment problem? Give examples.
5. Draw a network diagram for the following project plans. 6. For a set of 10 data points, the sum of the squared differences between the observed and estimated value of Y is 50. Given this information, what is the interpretation of the standard error of estimate?
7. The coefficient of correlation (or correlation coefficient) between two variables Y and X is -0.80. Calculate and interpret the value of the coefficient of determination.
8. Compute correlation coefficient between the variables X and Y from the given information and interpret it. n=15, ∑x=9027, ∑y=48.41, ∑xy=29321.96 ∑x2=5465631, ∑y2=157.6121.
9. Find slack and surplus values associated with each of the following constraints
MinZ=2×1+4×2
Subject to
x1+x2≤14
3×1+2×2≥30
2×1+x2≤18
x1,x2≥0 where MinZ=36 at x1=6 and x2=6
10. Formulate the following transportation problem in terms of linear programming problem with the cost matrix as Section “B”

Attempt any six questions.

11.The following shows the annual relationship between Research and Development and Profits from 2010 to 2015
Given the following information; a) Develop the estimating equation to predict the annual profits on the amount of budget for R&D.
If the firm spends Rs 8 million for R&D in 2020, what would be the expected annual profits during that year?
b) How much variation in annual profits is explained by the variation in the research expenditure?
c) Calculate the residual for the year 2012.

12.Bishal Bazar Supermarket has been expanding market share during the past 7 years, posting the gross sales in millions of rupees: The second-degree equation that best describes the secular trend for these data is y ̂=16.56+6.1x+0.82x^2 where 2003=0, x units=1 year
Calculate the percent of the trend for these data.
Calculate the relative cyclic residual for these data.
In which year does the largest fluctuation from the trend occur, and is it the same for both methods?
13. A manufacturing company manufactures two different products. The demand for both the products are strong so price as to realize a per-unit profit contribution of Rs. 16 on product A and Rs. 10 on product B. Each unit of product A requires four units of raw material, three units of labor, and two units of machine time. Each unit of product B requires two units of raw material, three units of labor, and five units of machine time. The firm has a daily supply of 24 units of raw material, 21 units of labor, and 30 units of machine time.
a) Formulate this LP problem
b) How much of each product manufactured to maximize total profit contribution?

14. a) From the following data calculate the price index number for 2010 with 2000 as a base by Fisher’s method. b) In a textile sales emporium, four salesman A, B, C, and D are available to four counters W, X, Y, and Z. each salesman can handle any counter. The service (in hours) of each counter when manned by each salesman is given below: How should the salesman be allocated to appropriate counters so as to minimize the service time? Each salesman must handle only one counter.

15. ‘Nepal Transport’ owns several trucks used to deliver crushed stones to road projects in the region. The company has received the delivery schedule for next week as follows: Find an optimum solution to minimize the transportation cost.

16. a) Write the dual of the following problem.
Minimize Z=3×1-5×2+4×3-9×4
Subject to the constraints:
X1-5×2+6×3+2×4≤12
4×1+7×2-2×3-3×4≤2
3×1-8×2+7×3-x4≥8
X1, x2, x3, x4≥0
b) The regression analysis resulted in the following ANOVA summary table for two independent variables: i. Determine whether there is a significant relationship between the Response variable (Y) and the two independent variables at the 0.05 level of significance.
ii. Compute the coefficient of multiple determinations and interpret its meaning.
17. A small project is composed of seven activities whose time estimates are given in the following table. a) Find the critical path and expected project length.
b) Find the standard deviation and variance of the critical path.
c) What is the probability that the project will be completed within 80 days?
d) What is the probability that the project will not be completed within 76 days?

Section “C”
Case Analysis

18. Police stations across the country are interested in predicting the number of arrests they can expect to process each month to better schedule office employees. Historically the average number of arrests (Y) each month is influenced by the number of officers on the police force (X1), the population of the city in thousand (X2), and the percentage of unemployed people (X3). The SPSS partial output for these factors in 15 cities are presented below: i. Using the above output, determine the best fitting regression equation. Also predict the value of an average number of arrests when there are 20 officers in the police force, the city’s population is 50,000 and 25% of the people are unemployed.
ii. At 0.01 level of significance which of the given independent variable is a better explanatory variable except for X2? Use the P-value approach in making your decision.
iii. Test at 0.01 level of significance, the overall fit of the model.
iv. Compute the standard error of estimate and interpret its meaning.

19.Robin Zill and Stewart Griffiths own a small company that manufactures portable massage tables in Hillsborough, North Carolina. Since they started the company, the number of tables they have sold is represented by this time series: a) Develop a 3-year moving average forecast for this time series. What is the forecast for the year 1995? Also, compute the MSE for the 3 years moving average.
b) Use alpha 0.2 to compute the exponential smoothing forecast values for the time series. What is the forecast for the year 1995? Also, calculate MSE as well.
c) Compare the 3-year moving average forecast with the exponential smoothing forecast using alpha 0.2. Which appears to provide a better forecast?

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