# Descriptive Statistics & Regression Analysis

Three quantitative reasoning statistics questions.

Problem 1: The following frequency table reports the number of employees in company using frequent flier miles (in thousands) during the first half of 2008.

Table 1. Frequent Flyer Data

Frequent Flier Miles (000) Number of Employees

0 up to 5 10

5 up to 10 22

10 up to 15 55

15 up to 20 821

20 up to 25 8

- How many employees were evaluated?

- What is the midpoint of the 4th class?

- Construct a histogram

- Interpret the outcome

Problem 2: Suppose you are in search for a minimum-wage job to help through school. After searching for a while, you found several jobs in your area that pay the hourly wages shown in Table 2.

(a) Perform numerical descriptive statistics and construct histogram, relative frequency diagram, cumulative frequency diagram, dot plot, steam and leaf plot, and a box plot for the hourly wage data.

(b) Interpret the results

Table 2. Hourly Wage Data ($)

Company Hourly Wages ($) Company Hourly Wages ($)

1 9.3 16 7

2 8.6 17 9.7

3 7.5 18 7.4

4 8.8 19 8.4

5 8.9 20 10.8

6 7.4 21 8.1

7 7.8 22 10.9

8 8.2 23 9.2

9 10.3 24 10.8

10 10 25 11.5

11 11.2 26 8.2

12 10.1 27 6.3

13 8.9 28 9.3

14 7.1 29 10.7

15 8 30 5.4

Problem 3: An auto rental company wanted to reach its maximum rental capacity of 10,000 cars during the weekends. One option was to reduce the weekend rate to encourage more people to rent. In order to determine what rate the company should use, data of a sample of historical weekend daily rental rates and the corresponding demand was collected. This data is shown in Table 3.

- Describe the relationship between the weekend daily rate and the rental demand

- What is the weekend daily rental rate that you think the company should use to reach its maximum rental capacity?

Table 3. Car Rental Rate and Corresponding Demand

Weekend Daily Rates ($) Number of Cars Rented

40 5000

30 5800

25 7100

16 9300

42 4800

18 7100

32 5700

26 6100

44 3600

16 7800

29 7000

16 9700

18 9990

38 5060

24 7300

31 5500

44 6900

17 6200

20 6000

40 5800

21 7800

16 8900

42 5320

20 8400

28 5900

18 8500

35 4298

Please see the attachment.

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#### Solution Summary

The solution provides step by step method for the calculation of descriptive Statistics and regression analysis. Formula for the calculation and Interpretations of the results are also included.