1. Using the function mp Sample TW, compute the average uniqueness of each label. What is the first-order serial correlation, AR(1), of this time series? Is it statistically significant? Why?

2. Fit a random forest to a financial dataset where

(a) What is the mean out-of-bag accuracy?

(b) What is the mean accuracy of k-fold cross-validation (without shuffling) on the same dataset?

(c) Why is out-of-bag accuracy so much higher than cross-validation accuracy? Which one is more correct / less biased? What is the source of this bias?

 

 

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1. Using the data in Table 2.3, calculate average fixed cost and average variable cost. Plot these on a graph with the average total cost and briefly explain the result.

2. When should a business cease production in the short run?

3. What costs need to be covered in the long run?

 

 

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1. ValarMorghulis Company was organized just a year ago. The normal capacity and actual production of the company is 2,500 units. The results of the company’s first year of operations are shown below.

ValarMorghulis Company

Income Statement

Sales (2,000 units sold)

P 135,000

Less: Cost of goods sold:

Beginning Inventory

P 0

Cost of Goods Manufactured

105,000

Goods Available for Sale

P 105,000

Ending Inventory

21,000

84,000

Gross Margin

51,000

Less: Selling and Administrative expenses

42,000

Net Income

P 9,000

The company’s unit variable cost is computed as follows:

Variable manufacturing cost

P 32

Variable Selling and Administrative expenses

5

Total Variable cost per unit

P 37

REQUIRED:

1. What is the Selling price per unit? Fixed MOH per unit application?

2. What is the total fixed manufacturing cost? Total fixed selling and administrative expense?

3. What the net income under full costing? Under direct costing?

 

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1. Victoria Ephanor manages a small product distribution company. Because the business is growing fast, Ephanor recognizes that it is time to manage the vast information pool to help guide the accelerating growth. Ephanor, who is familiar with spreadsheet software, currently employs a sales force of four people. She asks you to develop a data warehouse application prototype that will enable her to study sales figures by year, region, salesperson, and product. (This prototype is to be used as the basis for a future data warehouse database.) Using the data supplied in the Ch13_P2.xls file, complete the following seven problems: a. Identify the appropriate fact table components. (5) b. Identify the appropriate dimension tables. (5) c. Draw a star schema diagram for this data warehouse. (5) d. Identify the attributes for the dimension tables that will be required to solve this problem. (5) e. Using the spreadsheet generate a pivot table to show Sales by Product and by Region. The end user must be able to specify the display of Sales for any given Year. The sample oputput is shown below in Figure 1. f. Use problem (e) as your point of departure and add a second pivot table as in Figure 1 (on same spreadsheet) to show Sales by SalesPerson and by Region as in Figure 1 but the lower part. The end user must be able to specify Sales for a given Year or for ALL Years, and for a given Product or for ALL Products. (5) g. Create a 3D Bar Graph as part of your spreadsheet but give it a name CHART as in Figure 2 below. Your spreadsheet must therefore have at least three tabs. One for the raw data as given, one for the pivot tables and one for the CHART. The CHART must display as in Figure 2, the Sales for Salespeople within different Regions for each Product. (5) Figure 1: Pivot Tables showing Sales by Year AND Sales for Year and Product Figure 2: 3D- Bar Graph that shows Sales per Region for SalesPeople and Products

 

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1.We are given an array A containing n numbers, and an integer k that divides n. We want to find k numbers x1,x2, …,xk of A such that xi is the ( n /k i)-th smallest element of A. Develop a divide and conquer algorithm that finds the xi ’s that runs in time O(n lg k). Prove its correctness and running time.

2.Recall that the Fibonacci numbers are defined by the following recurrence: F0 = 0, F1 = 1 and Fn = Fn-1 + Fn-2 for n > 2. 1. Using the above recurrence, give a simple algorithm to compute Fn, given n. The complexity of the algorithm in terms of the number of arithmetic operations should be O(n 2 ). Show that the algorithm indeed has this complexity. Recall that an arithmetic operation is the cost of adding or multiplying two single digit numbers. (Hint: How many digits are there in Fn? Use the fact that Fn is T(( 1+v 5 2 ) n ). 2. Our goal is to use the following matrix identity to compute the nth Fibonacci number more efficiently. F1 F2 ! = 0 1 1 1! · F0 F1 ! (5.1) (a) Show that Fn Fn+1! = 0 1 1 1!n · F0 F1 ! (5.2) (b) Show that O(log n) matrix multiplications are enough to compute Fn. (c) Using the fast algorithm for multiplying two integers (Karatsuba’s algorithm) show that Fn can be computing in O(n log2 3 log n) arithmetic operations. (d) Can you improve your analysis of

(c) and show a cost of O(n log2 3 ) arithmetic operations ?

 

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