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# Intro Stats and Data Analysis ECON 2370

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This 5 page Class Notes was uploaded by Dr. Leon Koss on Saturday September 19, 2015. The Class Notes belongs to ECON 2370 at University of Houston taught by Staff in Fall. Since its upload, it has received 44 views. For similar materials see /class/208206/econ-2370-university-of-houston in Economcs at University of Houston.

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Date Created: 09/19/15

Econ 2370 Spring 2000 O Donnell 7 5 D 9 a 01 Chapter 3 Describing Bivariate Data Motivation Does the knowledge of the values of one variable help you understand the distribution of values of another variable How do you measure and assess this association a Economic theory tells us that price demanded falls as the available quantity of a good increase Supply of a good increases as prices rise Increasing the income of consumers for some goods can lead to an increase in price demanded for a good Discussion on causality does the association between two variables always imply causality Independent and dependent variables a Dependent variable variable of interest variations in the variable described by exploratory independent variables When theory describes a casuality be tween two variables values found in the dependent variable are heavily influenced caused by the exploratory or independent variables b Independent variables values found in an independent variable are not per ceived to be in uenced by other variables Does every association between variables imply that there exists an independent and dependent variable No No No Graphical presentation of bivariate data i The type of graphs used in economic textbooks are scatterplots 6 Tools to analyze the values in a scatterplot i Is there a pattern downward sloping pattern upward sloping pattern other patterns ii Clustering of the points along the pattern iii The presence of outliers 6 Numerical Measures of Bivariate data Interval variables xy 18 Econ 2370 Spring 2000 O Donnell a Correlation coef cient i Formula s smsy where 231931 i yd n l Say H H 39 Range ofr gt 1 to 1 H H H Interpretation of r gt 1 implies a very strong positive correlation scatterplot would show an upward sloping pattern with a tight clustering of points along the pattern 1 implies a very strong negative pattern 0 implies no pattern Note the value of r is not a measure of the slope 7 Using the correlation value to estimate the slope and intercept of the line that best represents the linear relationship between two variables Best tting line is called the regression line The best tting line is the line that gives the minimum distance between the points of data and the line The econometric course will examine how to produce the best tting line under different circumstances Let s take b to be the slope of the line and a as the intercept value the value where x20 The rst variable is x and its mean is i The second variable is y and its mean is g The formulas for b amp a are Inferences from Small Samples 1 lx39 00 F U The Central Limit Theorem which describes the mean standard deviation and shape of the sampling distribution depends on large samples n 2 30 What can be said about the mean standard deviation and shape of the sampling distribution when n is small If the sample is drawn from approximately normal populations the mean of the sampling distribution is the same for the sampling distribution of the means for large sample The shape is symmetric The standard deviation is not 1 it varies because the shape varies for different sample sizes Student s T scores distribution 1 2 Developed by WS Gosset in 1908 Based on a ratio of the standard normal distribution function and the square root of the X2 distribution 3 Given a sample of n observations the statistics t j 8 has a t distribution with n 1 degrees of freedom 1 There are many different If distributions 2 Every distribution resembles a standard normal distribution but each have fatter tails 3 Small samples have more variability 4 As the sample size approaches 30 the distribution becomes normal Degrees of Freedom 1 Number of independent units of observations in the sample relevant to estimation of a particular point estimate 2 There are n observations as the initial units of information 3 Only one observation is used to determine the point estimate 4 The remaining observations are allowed to be any value they are allowed to be free Mathematica Examples How do T scores compare to Z scores Here are the two tailed values at p005 Z Scores 196 TScores 1129 2045 df20 2086 1115 2131 1110 2228 if 5 2571

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