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Regression analysis to predict hourly wage

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This question refers to the estimated regressions in table 1 computed using data for 1988 from the U.S. Current Population Survey. The data set consists of information on 4000 full-time full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The worker's ages ranged from 25 to 34 years. The dataset also contained information on the region of the country where the person lived, marital status, and number of children. For the purposes of these exercises let
AHE = average hourly earnings (in 1998 dollars)
College = binary variable (1 if college, 0 if high school)
Female = binary variable (1 if female, 0 if male) Age = age (in years)
Ntheast = binary variable (1 if Region = Northeast, 0 otherwise)
Midwest = binary variable (1 if Region = Midwest, 0 otherwise)
South = binary variable (1 if Region = South, 0 otherwise)
West = binary variable (1 if Region = West, 0 otherwise)

a) Write a regression equation that uses these variables to predict average hourly earnings and be sure to define the Gender variable.

b) Explain how you avoid the dummy variable trap (Hint: why you omitted one regional variable and what happen if it is included).

c) Explain the important meanings of regional difference (compare to reference group).

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a) Write a regression equation that uses these variables to predict average hourly earnings and be sure to define the Gender variable.
Using the second regression (column two of the above table) we find:
Males: AHE=4.40 + 0.29 (X3)
Females: AHE= 4.40 -2.62 + 0.29 (X3) = 1.78 + 0.29 (X3)
This is the national average for wages for men and women, with age as a factor. To remove age as a factor, use the first regression. This gives you an average wage across all ...

Solution Summary

Using regression analysis to predict hourly wages for men and women in different regions of the country

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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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