Computing basic statistics

Lecture Basic statistics for business and economics - Chapter 14: Multiple regression analysis. After completing this chapter, students will be able to: Describe the relationship between several independent variables and a dependent variable using multiple regression analysis, develop and interpret an ANOVA table, compute and interpret measures of association in multiple regression,...

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R is a powerful tool for statistics and graphics, but getting started with this language can be frustrating. This short, concise book provides beginners with a selection of how-to recipes to solve simple problems with R. Each solution gives you just what you need to know to use R for basic statistics, graphics, and regression.

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When you have completed this chapter, you will be able to: Explain the concept of central tendency, identify and compute the arithmetic mean, compute and interpret the weighted mean, determine the median, identify the mode, explain and apply measures of dispersion, compute and explain the variance and the standard deviation.

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When you have completed this chapter, you will be able to: Construct and interpret a dot plot, identify and compute measures of position, construct and analyze a box plot, compute and describe the coefficient of skewness, create and interpret a scatter diagram, develop and explain a contingency table.

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When you have completed this chapter, you will be able to: Identify the characteristics of a probability distribution, distinguish between a discrete and a continuous random variable, compute the mean of a probability distribution, compute the variance and standard deviation of a probability distribution,...

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The main goals of this chapter are to: List the characteristics of the uniform distribution, compute probabilities by using the uniform distribution, list the characteristics of the normal probability distribution, convert a normal distribution to the standard normal distribution,...

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When you have completed this chapter, you will be able to: Define a point estimate, define confidence interval, compute a confidence interval for the population mean when the population standard deviation is known, compute a confidence interval for a population mean when the population standard deviation is unknown,...

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Chapter 15 - Nonparametric methods: Goodness-of-fit tests. After completing this chapter, students will be able to: Conduct a test of hypothesis comparing an observed set of frequencies to an expected distribution, list and explain the characteristics of the chi-square distribution, compute a goodness-of-fit test for unequal expected frequencies,...

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Chapter 3 - Describing data: Numerical measures. Learning objectives of this chapter include: Calculate the arithmetic mean, weighted mean, median, mode, and geometric mean; explain the characteristics, uses, advantages, and disadvantages of each measure of location; identify the position of the mean, median, and mode for both symmetric and skewed distributions; compute and interpret the range, mean deviation, variance, and standard deviation

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Chapter 4 - Describing data: Displaying and exploring data. After studying this chapter you will be able to: Construct and interpret a dot plot, identify and compute measures of position, construct and analyze a box plot, compute and describe the coefficient of skewness, create and interpret a scatter diagram, develop and explain a contingency table.

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Chapter 6 - Discrete probability distributions. After completing this unit, you should be able to: Identify the characteristics of a probability distribution, distinguish between a discrete and a continuous random variable, compute the mean of a probability distribution, compute the variance and standard deviation of a probability distribution,...

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Chapter 7: Continuous probability distributions. When you have completed this chapter you will be able to: List the characteristics of the uniform distribution; compute probabilities by using the uniform distribution; list the characteristics of the normal probability distribution; convert a normal distribution to the standard normal distribution;...

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Chapter 9 - Estimation and confidence intervals. In this chapter, students will be able to understand: Define a point estimate, define confidence interval, compute a confidence interval for the population mean when the population standard deviation is known, compute a confidence interval for a population mean when the population standard deviation is unknown,...

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Chapter 14 - Multiple regression analysis. This chapter include objectives: Describe the relationship between several independent variables and a dependent variable using multiple regression analysis; set up, interpret, and apply an ANOVA table compute and interpret the multiple standard error of estimate, the coefficient of multiple determination, and the adjusted coefficient of multiple determination.

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Chapter 15 - Nonparametric methods: Goodness-of-fit tests. When you have completed this chapter, you will be able to: Conduct a test of hypothesis comparing an observed set of frequencies to an expected distribution, list and explain the characteristics of the chi-square distribution, compute a goodness-of-fit test for unequal expected frequencies, conduct a test of hypothesis to verify that data grouped into a frequency distribution are a sample from a normal distribution,...

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Physicists pretend not only to know everything, but also to know everything bet- ter. This applies in particular to computational statistical physicists like US. Thus many of our colleagues have applied their computer simulation techniques to fields outside of physics, and have published sometimes in biological, economic or sociological journals, and publication flow in the opposite direction has also started.

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n these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations. From a point of view of data analysis, the concepts and techniques introduced here are of general interest and are, at best, employed by computational aid. Consequently, an exemplary implementation of the presented techniques using the Python programming language is provided.

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Monte Carlo methods are ubiquitous in applications in the finance and insurance industry. They are often the only accessible tool for financial engineers and actuaries when it comes to complicated price or risk computations, in particular for those that are based on many underlyings. However, as they tend to be slow, it is very important to have a big tool box for speeding them up or – equivalently – for increasing their accuracy. Further, recent years have seen a lot of developments in Monte Carlo methods with a high potential for success in applications.

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Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of financial derivatives, a need for sophisticated computational technology has developed. For example, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial differential equation.

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It was in late 1995 to early 1996 (shortly after the birth of his first daughter Claire) that the author first began to read the currently available finance books in order to write C/Cþþ financial software. However, apart fromthe book Options Futures and Other Derivatives by John Hull, he found very little information of practical help and had to trawl through the original journal articles in the Bodleian library for more information. Even then much information on how to implement and test various models was not included.

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