Stats 3000 Week 2 - Winter 2011
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Regression analysis allows researchers to identify an equation that best fits paired data and predict the relationship between two quantitative variables. Linear regression assumes a linear relationship and finds the line that best describes how the dependent variable changes with the independent variable. The regression line equation takes the form Y = bX + a, where b is the slope and a is the intercept. Researchers can use linear regression to predict new Y values based on X and assess how well the linear model fits the data.
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Kendall's ,partial correlation and scatter plot
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- Francis Galton carried out early work on correlation and his colleagues Karl Pearson developed methods to calculate correlation coefficients for parametric data.
- Correlation describes the relationship between two variables on a scale from -1 to 1, where -1 is a perfect negative correlation, 0 is no correlation, and 1 is a perfect positive correlation.
- Pearson's correlation coefficient r is commonly used to determine the strength and direction of correlation between two variables, with values between -0.6 and -1 or 0.6 and 1 indicating strong correlation.
- Correlation is widely used in research in physical education to analyze relationships between factors like physical performance and strength.
Simple correlation
1. The document discusses correlation and correlation coefficients, which measure the strength and direction of association between two variables.
2. A correlation coefficient ranges from 0, indicating no correlation, to 1 or -1, indicating perfect positive or negative correlation. Coefficients above 0.5 generally indicate a strong linear relationship.
3. The Pearson correlation coefficient (r) specifically measures the linear correlation between two normally distributed variables, while the Spearman correlation (rs) is nonparametric and assesses correlation between ordinal or non-normally distributed variables.
4. Correlation only indicates association, not causation. Significant correlation is also not necessarily clinically meaningful. Correlation coefficients and their statistical significance must be interpreted carefully.
2.5 correlation & best fitting lines
This document discusses identifying correlation in data by plotting it on a scatter plot and fitting a best-fit line. It explains that a positive slope indicates positive correlation, a negative slope indicates negative correlation, and no consistent slope indicates little correlation. It also introduces the correlation coefficient r as a measure of correlation strength, with values closer to 1 or -1 indicating stronger correlation.
Correlation ppt...
The document discusses correlation analysis and different types of correlation. It defines correlation as the linear association between two random variables. There are three main types of correlation:
1) Positive vs negative vs no correlation based on the relationship between two variables as one increases or decreases.
2) Linear vs non-linear correlation based on the shape of the relationship when plotted on a graph.
3) Simple vs multiple vs partial correlation based on the number of variables.
The document also discusses methods for studying correlation including scatter plots, Karl Pearson's coefficient of correlation r, and Spearman's rank correlation coefficient. It provides interpretations of the correlation coefficient r and coefficient of determination r2.
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Kendall's ,partial correlation and scatter plot
Kendall's tau is a nonparametric statistic that measures the ordinal association between two variables. It calculates the number of concordant and discordant pairs to determine the tau coefficient between -1 and 1, where higher positive values indicate a stronger monotonic relationship. Kendall's tau is often used as a hypothesis test of statistical dependence between variables and has advantages over Spearman's rho such as better statistical properties and direct interpretation. A partial correlation measures the relationship between two variables while controlling for one or more other variables. A scatter plot graphs the relationship between two quantitative variables with one on the x-axis and one on the y-axis to identify outliers, correlation, and the type of relationship.
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- Francis Galton carried out early work on correlation and his colleagues Karl Pearson developed methods to calculate correlation coefficients for parametric data.
- Correlation describes the relationship between two variables on a scale from -1 to 1, where -1 is a perfect negative correlation, 0 is no correlation, and 1 is a perfect positive correlation.
- Pearson's correlation coefficient r is commonly used to determine the strength and direction of correlation between two variables, with values between -0.6 and -1 or 0.6 and 1 indicating strong correlation.
- Correlation is widely used in research in physical education to analyze relationships between factors like physical performance and strength.
Simple correlation
1. The document discusses correlation and correlation coefficients, which measure the strength and direction of association between two variables.
2. A correlation coefficient ranges from 0, indicating no correlation, to 1 or -1, indicating perfect positive or negative correlation. Coefficients above 0.5 generally indicate a strong linear relationship.
3. The Pearson correlation coefficient (r) specifically measures the linear correlation between two normally distributed variables, while the Spearman correlation (rs) is nonparametric and assesses correlation between ordinal or non-normally distributed variables.
4. Correlation only indicates association, not causation. Significant correlation is also not necessarily clinically meaningful. Correlation coefficients and their statistical significance must be interpreted carefully.
2.5 correlation & best fitting lines
This document discusses identifying correlation in data by plotting it on a scatter plot and fitting a best-fit line. It explains that a positive slope indicates positive correlation, a negative slope indicates negative correlation, and no consistent slope indicates little correlation. It also introduces the correlation coefficient r as a measure of correlation strength, with values closer to 1 or -1 indicating stronger correlation.
Correlation ppt...
The document discusses correlation analysis and different types of correlation. It defines correlation as the linear association between two random variables. There are three main types of correlation:
1) Positive vs negative vs no correlation based on the relationship between two variables as one increases or decreases.
2) Linear vs non-linear correlation based on the shape of the relationship when plotted on a graph.
3) Simple vs multiple vs partial correlation based on the number of variables.
The document also discusses methods for studying correlation including scatter plots, Karl Pearson's coefficient of correlation r, and Spearman's rank correlation coefficient. It provides interpretations of the correlation coefficient r and coefficient of determination r2.
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The document discusses finding the line of best fit for a data set using linear regression. It explains that the line of best fit should have approximately the same number of points above and below the line. It also describes how the slope of the line indicates whether the correlation is positive, negative, or relatively no correlation. Finally, it introduces the correlation coefficient r as a measure of the strength of correlation, with values closer to 1 or -1 indicating a stronger correlation.
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This document is a presentation by Dwaiti Roy on partial correlation. It begins with an acknowledgement section thanking various professors and resources that helped in preparing the presentation. It then provides definitions and explanations of key concepts related to partial correlation such as correlation, assumptions of correlation, coefficient of correlation, coefficient of determination, variates, partial correlation, assumptions and hypothesis of partial correlation, order and formula of partial correlation. Examples are provided to illustrate partial correlation. The document concludes with references and suggestions for further reading.
Scatter diagram
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Correlation analysis ppt
Correlation analysis is used to find the degree of relationship between two or more variables by applying statistical tools. It produces a correlation coefficient that describes the strength and direction of the relationship. There are different types of correlation, including positive correlation where variables move in the same direction, negative correlation where they move in opposite directions, simple correlation between two variables, partial correlation controlling for other variables, and multiple correlation between three or more variables. Correlation analysis is important for measuring the degree of relationship between variables, estimating their values, and understanding economic behavior.
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Scattergrams
The document discusses scattergrams (also called scatterplots):
- A scattergram is a type of graph that uses Cartesian coordinates to display values for two variables from a data set, with each data point represented by a dot on the graph.
- Scattergrams are used to analyze patterns in bivariate data and show the distribution and relationship between two variables.
- Different patterns in scattergrams, like linearity, slope, and strength can indicate positive correlation, negative correlation, or no correlation between the variables.
Correlation analysis notes
To get a copy of the slides for free Email me at: japhethmuthama@gmail.com
You can also support my PhD studies by donating a 1 dollar to my PayPal.
PayPal ID is japhethmuthama@gmail.com
Correlation
Correlation and regression analysis are statistical tools used to analyze relationships between variables. Correlation measures the strength and direction of association between two variables on a scale from -1 to 1. Regression analysis uses one variable to predict the value of another variable and draws a best-fit line to represent their relationship. There are always two lines of regression - one showing the regression of x on y and the other showing the regression of y on x. Regression coefficients from these lines indicate the slope and intercept of the lines and can help estimate unknown variable values based on known values.
Correlation analysis
Correlation analysis examines the relationship between two or more variables. Positive correlation means the variables increase together, while negative correlation means they change in opposite directions. The Pearson correlation coefficient, r, quantifies the strength of linear correlation between -1 and 1. Multiple correlation analysis extends this to measure the correlation between one dependent variable and multiple independent variables. It is useful but assumes linear relationships and can be complex to calculate.
Math n Statistic
This document discusses methods for analyzing the relationship between two quantitative variables, including:
- Scatter diagrams can show the relationship and be used to identify if the variables are positively or negatively correlated.
- The linear correlation coefficient, r, quantifies the strength of the linear relationship between -1 and 1, where values closer to -1 or 1 indicate a stronger negative or positive correlation, respectively.
- Least-squares regression finds the best-fitting straight line to describe the linear relationship between two variables by minimizing the sum of the squared residuals. It can be used to make predictions, but may not be accurate far outside the original data range.
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application of correlation
This document discusses correlation analysis and different methods for studying correlation, including scatter diagram, Karl Pearson coefficient correlation, and Spearman's rank correlation methods. It defines the coefficient of correlation as a measure of the strength of the linear relationship between two variables based on their covariance and standard deviations. The coefficient r ranges from 1 to -1, indicating the magnitude and direction of the correlation. Strong correlations are considered r of .70 or higher and r of -.70 or lower, while weak correlations range from 0 to .30 and 0 to -.30.
Correlation analysis
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This document provides an introduction to linear regression analysis. It discusses how regression finds the best fitting straight line to describe the relationship between two variables. The regression line minimizes the residuals, or errors, between the predicted Y values from the line and the actual data points. The accuracy of predictions from the regression model can be evaluated using the correlation coefficient (r) and the standard error of estimate. Multiple linear regression extends this process to model relationships between a dependent variable Y and two or more independent variables (X1, X2, etc).
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This document discusses correlation and regression analysis techniques used in physical geography to examine relationships between variables. Correlation determines the degree of relationship between two variables and is represented by the correlation coefficient r, which ranges from -1 to 1. Regression identifies relationships between a dependent variable and one or more independent variables by calculating a best-fit line that minimizes residuals. The document provides examples of calculating the correlation coefficient r and estimating the regression equation between variables.
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The document discusses different types of correlation and methods for studying correlation. It describes Karl Pearson's coefficient of correlation, which measures the strength and direction of a linear relationship between two variables. The coefficient ranges from -1 to 1, where -1 is a perfect negative correlation, 0 is no correlation, and 1 is a perfect positive correlation. The document also discusses other types of correlation coefficients like Spearman's rank correlation coefficient and methods for analyzing correlation like scatter plots.
Partial correlation
This document is a presentation by Dwaiti Roy on partial correlation. It begins with an acknowledgement section thanking various professors and resources that helped in preparing the presentation. It then provides definitions and explanations of key concepts related to partial correlation such as correlation, assumptions of correlation, coefficient of correlation, coefficient of determination, variates, partial correlation, assumptions and hypothesis of partial correlation, order and formula of partial correlation. Examples are provided to illustrate partial correlation. The document concludes with references and suggestions for further reading.
Scatter diagram
A scatter plot displays values for two variables from a data set as a collection of points, with one variable determining the horizontal position and the other determining the vertical position. Scatter plots can reveal correlations between variables, such as positive, negative, or no correlation. They are useful for visualizing nonlinear relationships and comparing two data sets. An example shows lung capacity on the x-axis and breath holding time on the y-axis for a study of individuals.
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This document discusses correlation and different aspects of studying correlation. It defines correlation as the association or relationship between two variables that do not cause each other. It describes different types of correlation including positive, negative, linear, non-linear, simple, multiple and partial correlation. It also discusses various methods of studying correlation including graphic methods like scattered diagrams and correlation graphs, and algebraic methods like Karl Pearson's correlation coefficient and Spearman's rank correlation coefficient. The document explains concepts like coefficient of determination and hypothesis testing in correlation. It emphasizes that correlation indicates association but does not necessarily imply causation between variables.
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This presentation discusses correlation, rank correlation, bivariate analysis, and the chi-square test. Correlation measures the strength and direction of association between two variables. Rank correlation analyzes relationships between different rankings using Spearman's correlation coefficient. Bivariate analysis examines the empirical relationship between two variables. The chi-square test statistically tests if an observed distribution differs from an expected distribution using a chi-square distributed test statistic.
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The document discusses correlation and regression analysis. It defines correlation as the statistical relationship between two variables, where a change in one variable corresponds to a change in the other. The key types of correlation are positive, negative, simple, partial and multiple, and linear and non-linear. Regression analysis establishes the average relationship between an independent and dependent variable in order to predict or estimate values of the dependent variable based on the independent variable. Methods for studying correlation include scatter diagrams and Karl Pearson's coefficient of correlation, while regression analysis uses equations to model the linear relationship between variables.
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Correlation analysis is used to find the degree of relationship between two or more variables by applying statistical tools. It produces a correlation coefficient that describes the strength and direction of the relationship. There are different types of correlation, including positive correlation where variables move in the same direction, negative correlation where they move in opposite directions, simple correlation between two variables, partial correlation controlling for other variables, and multiple correlation between three or more variables. Correlation analysis is important for measuring the degree of relationship between variables, estimating their values, and understanding economic behavior.
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- Different patterns in scattergrams, like linearity, slope, and strength can indicate positive correlation, negative correlation, or no correlation between the variables.
Correlation analysis notes
To get a copy of the slides for free Email me at: japhethmuthama@gmail.com
You can also support my PhD studies by donating a 1 dollar to my PayPal.
PayPal ID is japhethmuthama@gmail.com
Correlation
Correlation and regression analysis are statistical tools used to analyze relationships between variables. Correlation measures the strength and direction of association between two variables on a scale from -1 to 1. Regression analysis uses one variable to predict the value of another variable and draws a best-fit line to represent their relationship. There are always two lines of regression - one showing the regression of x on y and the other showing the regression of y on x. Regression coefficients from these lines indicate the slope and intercept of the lines and can help estimate unknown variable values based on known values.
Correlation analysis
Correlation analysis examines the relationship between two or more variables. Positive correlation means the variables increase together, while negative correlation means they change in opposite directions. The Pearson correlation coefficient, r, quantifies the strength of linear correlation between -1 and 1. Multiple correlation analysis extends this to measure the correlation between one dependent variable and multiple independent variables. It is useful but assumes linear relationships and can be complex to calculate.
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This document discusses methods for analyzing the relationship between two quantitative variables, including:
- Scatter diagrams can show the relationship and be used to identify if the variables are positively or negatively correlated.
- The linear correlation coefficient, r, quantifies the strength of the linear relationship between -1 and 1, where values closer to -1 or 1 indicate a stronger negative or positive correlation, respectively.
- Least-squares regression finds the best-fitting straight line to describe the linear relationship between two variables by minimizing the sum of the squared residuals. It can be used to make predictions, but may not be accurate far outside the original data range.
coefficient correlation
The document presents a presentation on coefficient correlation by Irshad Narejo. It defines correlation as a technique used to measure the relationship between two or more variables. A correlation coefficient measures the degree to which changes in one variable can predict changes in another, though correlation does not imply causation. Correlation coefficient formulas return a value between -1 and 1 to indicate the strength and direction of relationships between data. Positive correlation means high values in one variable are associated with high values in the other, while negative correlation means high values in one variable are associated with low values in the other. The document discusses Pearson's correlation coefficient formula and provides an example of calculating correlation by hand versus using SPSS.
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This document discusses correlation analysis and different methods for studying correlation, including scatter diagram, Karl Pearson coefficient correlation, and Spearman's rank correlation methods. It defines the coefficient of correlation as a measure of the strength of the linear relationship between two variables based on their covariance and standard deviations. The coefficient r ranges from 1 to -1, indicating the magnitude and direction of the correlation. Strong correlations are considered r of .70 or higher and r of -.70 or lower, while weak correlations range from 0 to .30 and 0 to -.30.
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It is most useful for the students of BBA for the subject of "Data Analysis and Modeling"/
It has covered the content of chapter- Data regression Model
Visit for more on www.ramkumarshah.com.np/
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Discriminant analysis (DA) is a statistical technique used to predict group membership when the dependent variable is categorical and the independent variables are continuous. It identifies which variables discriminate between two or more naturally occurring groups. DA develops a linear equation to predict group membership based on weighted combinations of predictor variables. It aims to maximize the distance between group means to achieve strong discriminatory power. Like regression, DA assumes variables are normally distributed, cases are randomly sampled, and groups are mutually exclusive and collectively exhaustive. It requires at least two groups with minimal overlap and similar group sizes of at least five cases. DA can classify new cases into groups based on the discriminant functions derived from existing data.
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Linear regression
Correlation.pptx
This document discusses correlation and regression analysis. It defines correlation as a statistical measure of how related two variables are. A correlation coefficient between -1 and 1 indicates the strength and direction of the relationship. Scatterplots visually depict the relationship between variables. Regression analysis predicts the value of a dependent variable based on the value of one or more independent variables. The regression equation represents the line of best fit through the data points that minimizes the residuals.
correlationppt-111222215110-phpapp02.pdf
This document discusses correlation analysis and different correlation coefficients. It defines correlation as a linear association between two random variables. Correlation can be positive, negative, or zero. There are three main types of correlation: between two variables, linear vs nonlinear, and simple vs multiple vs partial. Methods for studying correlation include scatter plots, Karl Pearson's coefficient of correlation r, and Spearman's rank correlation coefficient. The coefficient of correlation r ranges from -1 to 1, while the coefficient of determination r^2 ranges from 0 to 1. Higher absolute r values indicate stronger correlation, while r^2 represents the percent of variation explained by the linear relationship.
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Syllabus
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Introduction to objective, scope and outcome the subject
Chapter 2
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Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
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- 2. Descriptive Methods in Regression Data comes in pairs of quantitative variables. Given such paired data (bivariate data), we want to determine whether there is a relationship between the two quantitative variables and, if so, identify what the relationship is. Regression analysis allows us to identify an equation that best fits the data, and to predict values of one variable based on another variable.
- 5. The goal is to be able to predict new values of Y based on values of X
- 9. Regression line: Line whose equation is used for prediction Line that best describes the relationship between y, the dependent variable and x, the independent variable. Describing a Straight Line Linear equation: When the relationship between X and Y is linear Linear equation: Y = bX + a
- 10. Linear regression builds on the equation for a straight line because the relationship between the two variables is assumed to be linear A straight line should yield the best “fit” of the data points in a scatterplot (a linear model)
- 17. Residuals - the difference between a score and its predicted value
- 24. A researcher suspects that there is a relationship between the number of promises a political candidate makes and the number of promises that are fulfilled once the candidate is elected. He examines the track record of 10 politicians. Use spss to construct a regression equation that predicts the number of promises made and promises kept by politicians.
- 30. slope The information in the column “unstandardized coefficients” column B embodies the regression equation: (constant) is the intercept
- 35. Scatterplot To see if scores may be related construct a graph of the scores, called a scatterplot The variable labeled X is plotted on the horizontal axis (the abscissa) The Y variable is plotted on the vertical axis (the ordinate) The score of a subject on each of the two measures is indicated by one point on the scatterplot
- 49. Direction of relationship A correlation coefficient indicates the direction of the relationship by the positive or negative sign of the coefficient A positive r indicates A positive (direct)relationship between variables X and Y As the scores on variable X increase, the scores on variable Y tend to increase A negative r indicates A negative (inverse)relationship between variables X and Y As the scores on variable X increase, the scores on variable Y tend to decrease
- 63. SPSS assignment # 2 due next week