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Descriptive Statistics, Bivariate and Linear Regression

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1. Using SPSS conduct descriptive statistics and provide a brief report. Your report should include descriptive statistics on all pertinent variables in the dataset (i.e. frequencies/percentages for nominal data; mean/median and standard deviations for continuous data). Include relevant tables in your write-up of the descriptive statistics.
2. Use SPSS to conduct bivariate analysis of the data and provide a brief report to include in the Results section. Find -correlation coefficients and p-values of FEV with age, sex, height and current smoke status. -whether there is a statistically significant difference between the mean of FEV with respect to the following: 1)gender and 2)smoking status. Include relevant tables and a description/interpretation of results.
3. Two simple linear regressions: 1) age as a predictor of FEV, and 2) height as a predictor of FEV. Describe and interpret the results (including the coefficients). Include the linear regression equations. How do the R values in linear regression relate to the correlation coefficient in the case of age and height?

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This solution is comprised of a detailed explanation of Descriptive Statistics, Bivariate Analysis, and Linear Regressions by using SPSS.

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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

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