...and weighted means, among other things. Chi-square Statistic. The chi-square statistic is used to measure the agreement between categorical data and a multinomial model that predicts the relative frequency of outcomes in each possible category. Suppose there are n independent trials, each of which can result in one of k possible outcomes. Suppose that in each trial, the probability that outcome i occurs is pi, for i = 1, 2, … , k, and that these probabilities are the same in every trial. The expected number of times outcome 1 occurs in the n trials is n×p1; more generally, the expected number of times outcome i occurs is expectedi = n×pi. If the model be correct, we would expect the n trials to result in outcome i about n×pi times, give or take a bit. Let observedi denote the number of times an outcome of type i occurs in the n trials, fori = 1, 2, … , k. The chi-squared statistic summarizes the discrepancies between the expected number of times each outcome occurs (assuming that the model is true) and the observed number of times each outcome occurs, by summing the squares of the discrepancies, normalized by the expected numbers, over all the categories: chi-squared = (observed1 − expected1)2/expected1 + (observed2 − expected2)2/expected2 + … + (observedk − expectedk)2/expectedk. As the sample size n increases, if the model is correct, the sampling distribution of the chi-squared statistic is approximated increasingly well by the chi-squared curve with (#categories − 1) = k − 1...
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...TITLE Determining the diversity of plant species communities on the forest interior and forest edge on the UTM campus and testing the association of two plant species; garlic mustard and Crown Vetch INTRODUCTION The underlying purpose of this field exercise was to determine the two main components of species diversity; richness and evenness. Richness is defined as the number of species along a transect while evenness is the dominance or distribution of species. In the first part of the exercise, In order to measure the richness (species diversity), 20m line transects were laid in the forest interior and forest edge on the UTM campus and the total number of individuals of each plant species were recorded. In the second part of the exercise, to measure the the association of two plant species; Garlic mustard and Crown vetch was determined by looking for the presence or absence of the species within the hoop. The hypothesis for the first part of the experiment would be that there will be higher species diversity on the forest edge. The prediction for the first exercise will be that more number of individuals will be found on the forest edge along the transect (richness) and the distribution of species will be highly uneven on the forest edge. The hypothesis for the second...
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...Abstract: The purpose of my project is to find out two things about students at my school: 1. Is hair related to eye color? 2. Is favorite color related to favorite ice cream flavor? I took a survey of students, and used the chi square (χ2) statistic to see if the data is related. The χ2 statistic showed that hair color and eye color are related, but favorite color and favorite ice cream flavor are not related. Purpose: To use statistics to find out two things about students at my school: 1. Is hair related to eye color? 2. Is favorite color related to favorite ice cream flavor? Research: I chose this project because I wanted to learn more about probability and statistics. I can use statistics to answer a question about students at my school. χ2 is used to compare sets of descriptive data. Descriptive data are things like colors, flavors, names, and other things that cannot be described by just a number, like height or weight. I picked hair color and eye color because I thought they would be related. I wanted to test this. I picked favorite color and favorite ice cream flavor because I didn’t think they would be related. I wanted to test this also. Hypotheses: First Hypothesis: Eye color and hair color will be related. In statistical terms: Null Hypothesis (H0): There is no relationship between eye color and hair color. Alternative Hypothesis (HA): There...
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...log-log model is as follows: Dependent Variable: LOG(TC) | | | Method: Least Squares | | | Date: 06/12/13 Time: 12:47 | | | Sample: 1 145 | | | | Included observations: 145 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | -3.526503 | 1.774367 | -1.987471 | 0.0488 | LOG(Q) | 0.720394 | 0.017466 | 41.24448 | 0.0000 | LOG(WAGE) | 0.436341 | 0.291048 | 1.499209 | 0.1361 | LOG(CAPITAL) | -0.219888 | 0.339429 | -0.647819 | 0.5182 | LOG(FUEL) | 0.426517 | 0.100369 | 4.249483 | 0.0000 | | | | | | | | | | | R-squared | 0.925955 | Mean dependent var | 1.724663 | Adjusted R-squared | 0.923840 | S.D. dependent var | 1.421723 | S.E. of regression | 0.392356 | Akaike info criterion | 1.000578 | Sum squared resid | 21.55201 | Schwarz criterion | 1.103224 | Log likelihood | -67.54189 | Hannan-Quinn criter. | 1.042286 | F-statistic | 437.6863 | Durbin-Watson stat | 1.013062 | Prob(F-statistic) | 0.000000 | | | | | | | | | | | | | | Solution 1: The estimated coefficients show the proportional change in total cost that results from proportional changes in firm’s output, changes in wages, changes in rental price of capital and changes in prices of fuel. | Estimated Coefficient | β2 | 0.720394 | β3 | 0.436341 | β4 |...
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...236263 | -4.546402 | 0.0001 | T | -0.023862 | 0.013049 | -1.828664 | 0.0785 | | | | | | | | | | | R-squared | 0.110203 | Mean dependent var | -1.455117 | Adjusted R-squared | 0.077248 | S.D. dependent var | 0.624716 | S.E. of regression | 0.600102 | Akaike info criterion | 1.883038 | Sum squared resid | 9.723306 | Schwarz criterion | 1.977334 | Log likelihood | -25.30405 | Hannan-Quinn criter. | 1.912570 | F-statistic | 3.344012 | Durbin-Watson stat | 2.469136 | Prob(F-statistic) | 0.078518 | | | | | | | | | | | | | | | | | | | | | | | | Signifikansnivået vurderes på bakgrunn av dette: “Alle forklaringsvariablene er signifikante fordi p-verdiene deres er mindre enn signifikansnivået på 5%” Beholder hvis p-verdien er under signifikansnivået. Alternativ 2: price c t Dependent Variable: PRICE | | | Method: Least Squares | | | Date: 05/03/11 Time: 10:27 | | | Sample: 1952 1982 | | | Included observations: 29 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | 0.418624 | 0.076877 | 5.445350 | 0.0000 | T | -0.008360 | 0.004246 | -1.969024 | 0.0593 | | | | | | | | | | | R-squared | 0.125564 | Mean dependent var | 0.285146 | Adjusted R-squared | 0.093178 | S.D....
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...1. 2. QBUS5001 3. QBUSS5002 topic1 - 12 EXCEL 4. word ----- 5. zh.lai@foxmail.com R-XIANG George Jackie HD QBUS5001 ~ Jack 2015/6/7 目录 ........................................................................................................................................................................................... 1 TOPIC 1 ....................................................................................................................................................................................... 4 TOPIC 2 PROBABILITY ........................................................................................................................................................ 4 2.1 EVENTS & PROBABILITIES 2.2 JOINT ............................................................................................................................................ 4 MARGINAL& CONDITIONAL PROBABILITIES 2.3 PROBABILITIES TREES ....................................................................................... 4 .......................................................................................................................................................... 4 2.4 BAYER’S THEOREM ......................................................................................................................................................................... 4 2.5 POPULATION MEAN & VARIANCE ................
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...Project of Econometrics INTRODUCTION In this paper our motivation to discuss effects of models by estimating its parameters in matrix and scalar notations, its variances checked via different formal and informal methods, checked the depends of error terms and analyze that auto-correlation whether it is positive, zero or negative, we also check the data is normality distributed or not, and check the structural stability. We consider the civilian unemployment rate and manufacturing hourly compensation in US dollars for simple regression. We consider the data in multiple regressions on Wildcat activity. Wildcats are wells drilled to find and produce oil and gas in an improved area or to find a new reservoir in a field previously found to be productive of oil or gas or to extend the limit of a known oil or gas reservoir. For hetroscedasticity tests we consider for simple regression wholesale and consumer price index data and for multiple regressions we take same data which we above used for multiple regression. We consider Fertility and other data for 64 countries for the F-test, Durbin-Watson test and CHOW test where child mortality depends upon the female literacy rate, per capita GNP and total fertility rate. DATA SOURCES I took the data from the Guajarati book. Table 5.10 on page no. 158 represents the data which we used for simple regression for hetroscedasticity tests. Table 7.7on page no. 237 represents the data which I used for multiple regressions. Table 6.4...
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...variables in the 3rd quarter of 2001. The same tests will be run as in the first model to compare and see whether any improvements to the model have been made. ------------------------------------------------- All variables appear statistically significant at the 95% level. They have their expected signs. The R bar square value is very high (.99806), as well as the F-stat (22135.4). Normal Distribution T-Test – Confidence Intervals P-Value | Similar to the previous model, the P-values for all 3 variables are 0.000. Since the value is less than 0.005, we reject the null hypothesis Ho and accept H1. The results are also statistically significant. There is 0% chance the null hypothesis is true. | Goodness of fit | Based on the R-bar squared figure of .99806. As the R-bar squared is above > 0.50, it also conforms to the third Gauss Markov assumption whereEUtVt-1=0, t≠t-1. | T-Ratio | From the results, * A: Serial Correlation*CHSQ ( 4) = 15.2797. This is not as bad as the value of 117.9066 obtained in the first model. | Normality | As can be seen from the results, C: Normality *CHSQ ( 2) = 289.8492. This exceeds the chi square critical value of 5.99 or 6 so we have to reject the normality of the model. | F-Distribution The F statistics can also be seen from the results above and have been compiled in the table below:...
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... | Exogenous: Constant | | | Lag Length: 0 (Automatic based on SIC, MAXLAG=23) | | | | | | | | | | | | | | t-Statistic | Prob.* | | | | | | | | | | | Augmented Dickey-Fuller test statistic | -35.96681 | 0.0000 | Test critical values: | 1% level | | -3.434655 | | | 5% level | | -2.863328 | | | 10% level | | -2.567771 | | | | | | | | | | | | *MacKinnon (1996) one-sided p-values. | | | | | | | | | | | | Augmented Dickey-Fuller Test Equation | | Dependent Variable: D(LOG_RETURNS) | | Method: Least Squares | | | Date: 11/03/10 Time: 16:06 | | | Sample (adjusted): 1/04/2005 11/02/2010 | | Included observations: 1449 after adjustments | | | | | | | | | | | | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | LOG_RETURNS(-1) | -0.944031 | 0.026247 | -35.96681 | 0.0000 | C | 0.000692 | 0.000484 | 1.429639 | 0.1530 | | | | | | | | | | | R-squared | 0.472016 | Mean dependent var | 1.64E-07 | Adjusted R-squared | 0.471651 | S.D. dependent var | 0.025333 | S.E. of regression | 0.018414 | Akaike info criterion | -5.150009 | Sum squared resid | 0.490653 | Schwarz criterion | -5.142723 | Log likelihood | 3733.181 | Hannan-Quinn criter. | -5.147290 | F-statistic | 1293.611 | Durbin-Watson stat | 1.996888 | Prob(F-statistic) | 0.000000 | | | | | | | | | | | | | | ...
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...THE RELATIONSHIP BETWEEN STOCK MARKET AND ECONOMIC GROWTH IN ASEAN COUNTRIES BY KOH YONG HONG CHOONG PIK SIN LEE SOCK MEI NG HON MENG LEONG MUN HONG A research project submitted in partial fulfillment of the requirement for the degree of BACHELOR OF BUSINESS ADMINISTRATION (HONS) BANKING AND FINANCE UNIVERSITI TUNKU ABDUL RAHMAN FACULTY OF BUSINESS AND FINANCE DEPARTMENT OF FINANCE MARCH 2016 Copyright @ 2016 ALL RIGHTS RESERVED. No part of this paper may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, graphic, electronic, mechanical, photocopying, recording, scanning, or otherwise, without the prior consent of the authors. DECLARATION We hereby declare that: (1) This undergraduate research project is the end result of our own work and that due acknowledgement has been given in the references to ALL sources of information be they printed, electronic, or personal. (2) No portion of this research project has been submitted in support of any application for any other degree or qualification of this or any other university, or other institutes of learning. (3) Equal contribution has been made by each group member in completing the research project. (4) The word count of this research report is 10,786 words. Name of Student: Student ID: Signature: 1. KOH YONG HONG 11ABB02521 2. CHOONG PIK...
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...INTERPRETATIONS of RESULTS The chi squared test is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is true. Thus in other terms, we compare observed data we expected to obtain according to our hypothesis. In this test we can see how to reject or accept the null hypothesis, and we can see that by X2calc being greater than the number we get obtain from the table of critical values. And if that number that we try t figure out is larger, than we have to reject our events being independent. And that basically says that our information, or our hypothesis is wrong. The excepted values that we interpreted was if everyone one didn’t miss the shots, and made them, then we would have excepted those results in our data. They represent the values if nothing went wrong, or in this case, if none of the girls missed the shots. | shots made | shots missed | total | left | 11 | 9 | 20 | Right | 15 | 5 | 20 | | 26 | 14 | 40 | My raw data presented was of the girls and how much they made or missed their shots with their left or right foot. The purpose behind this was too see if they can kick better with the dominate or non-dominate leg. And the result of this was my value of x2 and how it was smaller than 3.84. my value was 3.05, so my null hypothesis was accepted that right and left are independent. | shots made | shots missed | left | 25.5 | -0.15 | right...
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...The terms "statistical analysis" and "data analysis" can be said to mean the same thing -- the study of how we describe, combine, and make inferences based on numbers. A lot of people are scared of numbers (quantiphobia), but data analysis with statistics has got less to do with numbers, and more to do with rules for arranging them. It even lets you create some of those rules yourself, so instead of looking at it like a lot of memorization, it's best to see it as an extension of the research mentality, something researchers do anyway (i.e., play with or crunch numbers). Once you realize that YOU have complete and total power over how you want to arrange numbers, your fear of them will disappear. It helps, of course, if you know some basic algebra and arithmetic, at a level where you might be comfortable solving the following equation There are three (3) general areas that make up the field of statistics: descriptive statistics, relational statistics, and inferential statistics. 1. Descriptive statistics fall into one of two categories: measures of central tendency (mean, median, and mode) or measures of dispersion (standard deviation and variance). Their purpose is to explore hunches that may have come up during the course of the research process, but most people compute them to look at the normality of their numbers. Examples include descriptive analysis of sex, age, race, social class, and so forth. 2. Relationalstatistics fall into one of three categories: univariate,...
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...competitive and make a profit. The recent history of struggles they have encountered mainly due to the economy, fuel costs, and also the structural damage of the aircraft. Southwest has had to develop and execute plans to improve their business to retain a strong company. Southwest’s management team has requested a research team using a survey as the main instrument to help understand the airlines travelers concerns and desires to prevent them from seeking travel to other airlines. The research conducted will provide management with some insight into the reasons travelers will continue to utilize southwest as there primary airline of choice. BACKGROUND Southwest Airlines has built its culture and its reputation from the inside out. It values a happy workforce, and believes that its 32,000 satisfied employees will keep customers coming back. Southwest sees the importance of building and sustaining strong internal relationships. They believe in promoting from within and providing employees the opportunity to grow and learn from one another. Everyone at Southwest understands the role each individual plays and how each and every employee contributes to the company's success. Information flows freely between employees and leadership, and this is especially important in an industry as heavily unionized as the airline industry. Given the focus on quality in traditional manufacturing environments, it is no surprise that tangible goods such as automobiles, soft drinks,...
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...Abstract As shown in previous research a relationship between tuition fee and student enrollment exists, this study focusses on this relationship moderated by government aid and career expectations. By manipulating these variables in a questionnaire with vignettes all other variables able to influence this relationship are controlled as much as possible. Results suggest that a variation in both government aid and career expectation influence students’ decision to enroll both for their first study as for a further study after graduation. The effect of career expectations seems to be the most crucial on a student’s enrollment choice. How career expectations, tuition fees and government aid impact student enrollment Education in all its forms is one of the fundamental elements of societies. By educating people a society can function and develop. This is especially the case in western countries in which knowledge, which can be acquired through education is of crucial importance. The need for high educated persons is of great importance for western countries such as member states of the European Union. The importance of higher education is reflected in strategies launched by the European Union (Rodriguez, al, 2010; European Commission, 2010), aiming towards a knowledge economy and becoming more competitive in future years. This vision is also being shared outside the European Union (Yang, 2011). The tuition fees in the Netherlands are rising and...
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...be manually added in one table. There is to be an interpretation at the end of each table which includes concerns about the differences in the mean prices and mean mpg across vehicle types and the possible causes depending on whether it’s a mpg or price table. The distribution of price and mpg shapes across each vehicle type and what it means. Confidence intervals are to be used to talk about prices in the population of cars. Several differences of means tests on both prices and mpg are to be taken where there is no much difference between the means of different car types, in both prices and mpg. To find the likelihood of a cheap car of an efficient car across categories probability is to be used and its pattern is to be tested using chi squared tests. The second aim is to predict the mpg. This is to be done by using correlation to look for linear...
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