History Regression analysis is a statistical tool for investigating the relationship between variables. It is frequently used to predict the future and understand which factors cause an outcome. The legendary German mathematician Carl Friedrich Gauss claimed his alleged discovery of statistical regression. The method seemed so obvious to Gauss that he figured he must not have been the first to use it. He was sure enough it must have been discovered that he did not publicly state his finding until many years later, after his contemporary Adrien-Marie Legendre had published on the method. When Gauss suggested he had used it before Legendre it set off “one of the most famous priority disputes in the history of science...” Gauss would eventually …show more content…
First, linear regression needs the relationship between the independent and dependent variables to be linear. It is also important to check for outliers since linear regression is sensitive to outlier effects. The linearity assumption can best be tested with scatter plots, the following two examples depict two cases, where no and little linearity is present. 2. Secondly, the linear regression analysis requires all variables to be multivariate normal. This assumption can best be checked with a histogram or a Q-Q-Plot. Normality can be checked with a goodness of fit test, e.g., the Kolmogorov-Smirnov test. When the data is not normally distributed a non-linear transformation (e.g., log-transformation) might fix this issue. 3. Thirdly, linear regression assumes that there is little or no multicollinearity in the data. Multicollinearity occurs when the independent variables are too highly correlated with each other. 4. Fourth, linear regression analysis requires that there is little or no autocorrelation in the data. Autocorrelation occurs when the residuals are not independent from each other. For instance, this typically occurs in stock prices, where the price is not independent from the previous price.
Inferential Statistics has two approaches for making inferences about parameters. The first approach is the parametric method. The parametric method either knows or assumes that the data comes from a known type of probability distribution. There are many well-known distributions that parametric methods can be used, such as the Normal distribution, Chi-Square distribution, and the Student T distribution. If the underlying distribution is known, then the data can be tested accordingly. However, most data does not have a known underlying distribution. In order to test the data parametrically, there must be certain assumptions made. Some assumptions are all populations must be normal or at least same distribution, and all populations must have the same error variance. If these assumptions are correct, the parametric test will yield more accurate and precise estimates of the parameters being tested. If these assumptions are incorrect, the test will have a very low statistical power. This will reduce the probability of rejecting the null hypothesis when the alternative hypothesis is true. So what happens with the data is definitely known not to fit any distribution? This is when nonparametric methods are used.
Gauchos are the cowboys of Brazil, Argentina, and Uruguay. In the past, gauchos were very poor. The people who owned the ranches did not want beef. There were no refrigerators to keep the meat, so they could not sell it. As a result, the Gauchos ate meat three times a day. Today gauchos still work in South America but their lives are much better than they were in the past.
It was only a few years after Galileo's time that the scientific method was developed, and it was not until years later that the scientific method was a recognizable method of study. Had the scientific method been a concept when Galileo's ideas were first brought about, the church may have paid more attention to his scientific ideas, and therefore been more open to the ideas he presents in his letter to the Duchess.
In addition to theories causality, the quality of the empirical test is important. A theory that doesn’t measure the independent and dependent variables correctly could cause inadequate methodological quality. Also, it could cause issues with hypothesising. Furthermore, if the theory doesn’t collect enough data from a related, large and diverse sample then the theory is insufficient. All of these pieces correlate to contribute to a sufficient empirical test. For example, if a theory suggests all men who grow up in a violent house hold will commit violent acts in the future, but doesn’t collect data from a large enough population or includes women in the study then their empirical testing could be insignificant, which would lead to the theory not being empirically valid.
the empirical test of the hypothesis requires at least one or more background assumptions or
One source of this interest in method was ancient mathematics. The thirteen books of Euclid's Elements was a model of knowledge and deductive method. But how had all this been achieved? Archimedes had made many remarkable discoveries. How had he come to make these discoveries? The method in which the results were pr...
The dependent variables rely on the independent variables:
Scatter plots are similar to line graphs in that they both use horizontal and vertical axes to plot data points. The closer the data aims to making a straight line, the higher the correlation between the two variables, or the stronger the relationship(MSTE,n.d) The scatter plot above does not have a straight line formation, so that showing that there is not a strong relationship between the two variables of GPA and final.
In evaluating statistical data one thing to consider is the measure that is used. By understanding the different statistical measurement tools and how they differ from one another, it is possible to judge whether a statistical graph can be accepted at face value. A good example is using the mean to depict averages. This was demonstrated by using the mean as a measure of determining the distribution of incomes. The mean income depicted was, $70,000 per year. At face value, it looks as though the sample population enjoys a rather high income. However, upon seeing individual salaries, it becomes obvious that only a few salaries are responsible for the high average income as depicted by the mean. The majority of the salaries were well under the $70,000 average. Therefore, the mean distributed income of $70,000 was at best misleading. By also looking at the median and mode measures of the income distributions, one has a clearer picture of the actual income distributions. Because this data contained extreme values, a standard deviation curve would have given better representation of salary distribution and would have highlighted the salaries at the high level and how they skewed the mean value.
slope. I think that out of all the variables, this is the one which is
improved by Aristotle. But Galileo came up with a new argument named heliocentrism. In a long
Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the actual problem being studied.
Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quartic.
Analytics means using data and performing statistical analysis on it, applying quantitative and predictive models, in order to arrive at a certain decision. Analytics can be the first step in a process or can rather be an intermediate step as well. Analysis can be done using different set of tools that are available in the market or it can done manually using different concept and formulas. Business intelligence firms like Cognos, SAS and BusinessObjects have developed different tools that are readily available in market that assist in analysis and decision making. Analytics is used in order to find solutions to the problems and the solutions provided enables us to be successful and in the business world allow us to compete with our contenders.
There are many people that contributed to the discovery of irrational numbers. Some of these people include Hippasus of Metapontum, Leonard Euler, Archimedes, and Phidias. Hippasus found the √2. Leonard Euler found the number e. Archimedes found Π. Phidias found the golden ratio. Hippasus found the first irrational number of √2. In the 5th century, he was trying to find the length of the sides of a pentagon. He successfully found the irrational number when he found the hypotenuse of an isosceles right triangle. He is thought to have found this magnificent finding at sea. However, his work is often discounted or not recognized because he was supposedly thrown overboard by fellow shipmates. His work contradicted the Pythagorean mathematics that was already in place. The fundamentals of the Pythagorean mathematics was that number and geometry were not able to be separated (Irrational Number, 2014).