This page shows an example of poisson regression analysis with footnotes explaining the output. The data collected were academic information on 316 students. The response variable is days absent during the school year (daysabs), from which we explore its relationship with math standardized tests score (mathnce), language standardized tests score (langnce) and gender . As assumed for a Poisson model our response variable is a count variable and each subject has the same length of observation time. Had the observation time for subjects varied, the Poisson model would need to be adjusted to account for the varying length of observation time per subject. This point is discussed later in the page. Also, the Poisson model, as compared to other count models (i.e., negative binomial or zero-inflated models), is assumed the appropriate model. In other words, we assume that the dependent variable is not over-dispersed and does not have an excessive number of zeros. The first half of this page interprets the coefficients in terms of Poisson regression coefficients and the second half interprets the coefficients in terms of incidence rate ratios.

We also run the estat ic command to calculate the likelihood ratio chi-square statistic.

...ANALYSIS OF SICKNESS ABSENCE USING POISSONREGRESSION MODELS David A. Botwe, M.Sc. Biostatistics, Department of Medical Statistics, University of Ibadan Email: davebotwe@yahoo.com
ABSTRACT Background: There is the need to develop a statistical model to describe the pattern of sickness absenteeism and also to predict the trend over a period of time. Objective: To develop a statistical model that adequately describes the pattern of sickness absenteeism among workers. Setting: University College Hospital (UCH), Ibadan, Nigeria. Methodology: A retrospective study involving a review of sickness records of all workers in UCH between January and December 2003 was carried out. Data were extracted from the staff records of the Staff Medical Services Department. Independent samples t-tests and one-way analysis of variance tests were used to test for statistically significant differences in the mean number of spells and duration between various groups of workers. Poissonregression models were fitted to describe the pattern of the number of spells of sickness. Results: Out of 3309 workers, 240 had records of sickness absenteeism, giving a prevalence rate of 7.3%. The mean spells of sickness was 3 spells per absentee per year, while the mean duration of absence was 4 days per absentee per year. Females had a significantly higher number of spells than males (p = 0.009) and longer duration of absence than males (p = 0.015). No...

...Cox Regression Models
Questions with Answers Worked Example
An investigation is carried out into popularity of new cars being bought in the showroom of a Mercedes dealer. Data recorded for each car included colour, engine size and car type. A Cox proportional hazards model was ﬁtted to the data and the results are given below:
Write down the Cox hazard function according to this model. With regards to the model you have written down above state the following: • To which class of car does the baseline hazard refer • Which car has the lowest hazard rate • Which car has the highest hazard rate
1
Exercises
1. Suppose the lifetime, the age and sex of a number of lives are recorded and the Cox model is ﬁtted by maximising the partial likelihood. The ﬁtted parameters are βf = −0.5 where f denotes a female life and βa = 0.01 denoted the is the age eﬀect in years. Taking a male aged 40 as the reference hazard calculate the ratio of the hazards for (a) a male aged 20, (b) a male aged 60, (c) a female aged 20, (d) a female aged 60. 2. A study has been carried out to investigate the factors aﬀecting the survival times of mice suﬀering from leukaemia. A sample of 42 mice was divided into two equal groups - a treatment and a control group. The data available in respect of each mouse are: • survival time in weeks • group (0=treatment, 1=control) • sex (0=male, 1=female) • log WBC (WBC=white blood count) The results of two particular ﬁtted Cox models are given:...

...Regression Analysis: A Complete Example
This section works out an example that includes all the topics we have discussed so far in this chapter.
A complete example of regression analysis.
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A random sample of eight drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums.
Driving Experience (years) Monthly Auto Insurance Premium
5 2 12 9 15 6 25 16
$64 87 50 71 44 56 42 60
a. Does the insurance premium depend on the driving experience or does the driving experience depend on the insurance premium? Do you expect a positive or a negative relationship between these two variables? b. Compute SSxx, SSyy, and SSxy. c. Find the least squares regression line by choosing appropriate dependent and independent variables based on your answer in part a. d. Interpret the meaning of the values of a and b calculated in part c. e. Plot the scatter diagram and the regression line. f. Calculate r and r2 and explain what they mean. g. Predict the monthly auto insurance premium for a driver with 10 years of driving experience. h. Compute the standard deviation of errors. i. Construct a 90% confidence interval for B. j. Test at the 5% significance level whether B is negative. k. Using α = .05, test whether ρ is different from zero.
Solution a. Based on theory and intuition, we...

...Regression Analysis (Tom’s Used Mustangs)
Irving Campus
GM 533: Applied Managerial Statistics
04/19/2012
Memo
To:
From:
Date: April 19st, 2012
Re: Statistic Analysis on price settings
Various hypothesis tests were compared as well as several multiple regressions in order to identify the factors that would manipulate the selling price of Ford Mustangs. The data being used contains observations on 35 used Mustangs and 10 different characteristics.
The test hypothesis that price is dependent on whether the car is convertible is superior to the other hypothesis tests conducted. The analysis performed showed that the test hypothesis with the smallest P-value was favorable, convertible cars had the smallest P-value.
The data that is used in this regression analysis to find the proper equation model for the relationship between price, age and mileage is from the Bryant/Smith Case 7 Tom’s Used Mustangs. As described in the case, the used car sales are determined largely by Tom’s gut feeling to determine his asking prices.
The most effective hypothesis test that exhibits a relationship with the mean price is if the car is convertible. The Regression Analysis is conducted to see if there is any relationship between the price and mileage, color, owner and age and GT. After running several models with different independent variables, it is concluded that there is a relationship between the price and...

...Simple Linear Regression in SPSS
1.
STAT 314
Ten Corvettes between 1 and 6 years old were randomly selected from last year’s sales records in Virginia Beach, Virginia. The following data were obtained, where x denotes age, in years, and y denotes sales price, in hundreds of dollars. x y a. b. c. d. e. f. g. h. i. j. k. l. m. 6 125 6 115 6 130 4 160 2 219 5 150 4 190 5 163 1 260 2 260
Graph the data in a scatterplot to determine if there is a possible linear relationship. Compute and interpret the linear correlation coefficient, r. Determine the regression equation for the data. Graph the regression equation and the data points. Identify outliers and potential influential observations. Compute and interpret the coefficient of determination, r2. Obtain the residuals and create a residual plot. Decide whether it is reasonable to consider that the assumptions for regression analysis are met by the variables in questions. At the 5% significance level, do the data provide sufficient evidence to conclude that the slope of the population regression line is not 0 and, hence, that age is useful as a predictor of sales price for Corvettes? Obtain and interpret a 95% confidence interval for the slope, β, of the population regression line that relates age to sales price for Corvettes. Obtain a point estimate for the mean sales price of all 4-year-old Corvettes. Determine a 95% confidence...

...and French(1992) found that SMB and HML effect the risk premium of risk asserts. So they added the two risk factors into CAPM model. The Fama-French model can be read as:
Rit-Rft=αi+β1 (Rmt-Rft)+β2SMB+β3HML+εi
To better exam the performance of mutual funds, this project adds momentum factor which was put forward by Carhart (1997) and traded liquidity factor suggested by Pastor and Stambaugh (2003) into the Fama-French model. The model is defined as:
Rit-Rft=αi+β1 (Rmt-Rft)+ β2SMB+β3HML+β4mom+β5TradedLIQ+εi
Regression analysis
Before regress multi-fund asset-pricing models, multicollinearity should be tested. The highly imperfect multicollinearity leads to large variance and covariance of OLS estimators. The t-statistics of OLS estimators tend to not statistically significant and the confidence interval will be wide a lot.Usually there are no highly correlations between all independent variables if the values are less than 0.5.
After running the OLS regression, autocorrelation should be tested. Autocorrelation leads to OLS no longer efficient even though OLS still consistent and unbiased and the t-statistic, p-value is not accurate. In this project, Breusch-Godfrey Serial Correlation LM Test used to test autocorrelation. When the probability of chi-square is bigger than 0.5, the null hypothesis is accepted at 5% significance level, that means, there is no autocorrelation in the model.
Additionally, if a model has heteroskedasticity, the...

...Park University
Multiple Regression Analysis
Pamela Lima
EC315 Quantitative Research Methods
Dr. Bell
11/22/2013
Multiple Regression Analysis
Miami Heat Average Attendance per season
Miami Heat History
The Miami Heat is a professional basketball team, based in Miami, Florida. The team is a member of the Southwest Division in the Eastern Conference of the National Basketball Association (NBA). The Miami Arena was the home of the Heat until the end of the 1999.
The American Airlines Arena, located in Downtown Miami is the new home of the Heat since January 2nd, 2000. Micky Arison is the team owner; he also owns the giant Carnival cruise lines. Pat Riley is the team president and general manager, and Erik Spoelstra is the head coach. Their mascot is Burnie, an anthropomorphic fireball.
The Miami Heat team was formed in 1988; the Heat has won three league championships so far (2006, 2012, and 2013). They also added four conference titles, and 10 division titles. With 27 wins in a row between February 3 to March 27, 2013 the Heat hold the second-longest streak in NBA history. In 2013, Forbes Magazine valued the Heat at $625 million.
Leading the recent winning tradition that the Heat had achieved are LeBron Raymone James, and Dwayne Wade. Together they are responsible for most part of the points scored by the Heat. “King James”, as he is called by the Miami Heat fans is their star player and actual NBA Most Valuable...

...A regression analysis of the number of establishments in the florists industry
Industry Description
Operators in the United States florists industry retail cut flowers, floral arrangements and potted plants. They purchase these products from domestic and international firms and sell them mostly to the local population. Currently, the traditional forists suffer from severe competition form online stores and supermarkets. This results in a decreasing number of florists establishments in the United States; in the period of 1993 until 1997, the number of establishments decreased by 2.6 percent (Carree, 2002). This trend became stronger; from 2005 until 2010, the number of establishments decreased by 3.5 percent. (IBIS World, 2010). Since the industry of traditional florists suffers, an increasing number of traditional florists tries to make op for these losses by pooling their forces together and creating a national wire of florists (IBIS World, 2010).Consequently, concentration within this industry might be enforced, leading to higher entry barriers. However, that is not yet the case. According to the Carree (2002), the florists industry has a very low ratio of 1.05 of the number of establishments to the number of firms in 1997. This indicates that firms that own multiple establishments are quite rare in this industry.
In 1997, there were 26,505 establishments in the florists industry having payroll in...