Statistics: Correlation and Linear Regression

Preview (3 of 7 Pages)

100%

Statistics: Correlation and Linear Regression - Page 1 preview image

Loading page ...

Page1of7StatisticsDr S. TherianosCorrelationand Linear RegressionCorrelation:A technique used to decide whether there is a statistically significantlinearrelationship between the values of the dependent and independent variables.Regression:A statistical method used to describe the nature of the relationship betweenthe dependent and independent variables witha linear equation, called theRegressionLine.Association:A vague term used to describe the relationship between two variables.We shall investigate relationships between variables.If only two variables are involved the relationship issimple.For example, is there a relationship between a person’s age and his or her bloodpressure?If more than two variables are studied we have amultiple relationship.For example a student’s success in college depends on many factors such as the hoursdevoted to studying, the GPA, high school background, social and economic conditions.In this course we study onlysimple relationships.There are many types of relationships:Arelationshipispositiveif both variables increase or decrease at the same time.For example there is a positive relationship between a person’s height and weight.A relationship isnegativeifone variable increases and the other decreases, or viceversa.For example, for older people, as age increases, in general, agility decreases.Also, a relationship can belinearornonlinear.Our purpose is to answer the following questions statistically:1.Is there an association between the variables?Basically this means arethetwo variablesx and ysomehowrelated?2. If the variables are related, what is thetype or shapeof the relationship?

Statistics: Correlation and Linear Regression - Page 2 preview image

Loading page ...

Statistics: Correlation and Linear Regression - Page 3 preview image

Loading page ...

Page2of7This means is the relationship linear or non-linear? Is it positive or negative?To answer these two questions we plot the points (x, y).The resulting graph is called ascatter plot,orscatter diagramorscatter-gram.3.If the scatter plot shows a linear relationship orcorrelationhow do we measure it?The strength of thelinearrelationship is measured by a number called thelinearcorrelation coefficient r.4. What kind of predictions can be made from the relationship?Predictions are made all the time and in all areas, including weather forecasting, stockmarket, sales predictions, crop predictions, sports, energy, global warming, health etc.Some predictions are more accurate than others depending on the strength of therelationship between the variables andthe honesty of the researcher.You probably read about the “scientists” that conveniently omitted certain data that didnot support their predictions about global warming.Scatter Plots:The existence of a relationship between two variables can be visually determined byascatterplotorscatterdiagram.Def:AScatterPlotis agraphof ordered pairs of sample data.The points are plotted but they are not joined together.The Independent variable is always on the Horizontal axis.The Dependent variable is always on the Vertical axis.The purpose of ascatterdiagram is to give us a visual representation of the pairs of dataand help us determine if there is any “pattern”.As the x-values increase do the y-values increase, or decrease, or do the y-values seemcompletely unaffected. To put it in another way a scatter diagram shows if there is anycorrelationbetween the values of the dependent and theindependent variables.Consider the following scatter diagram.There appears to be a “linear pattern” or“linear trend".It seems that we can draw a straight line that approximates all thepoints. This line is called theRegression line.We shall compute its equationlater.Ex. 1:Construct a scatter diagram for the following pairs of points:x1.01.52.02.53.03.54.04.55.06.0y0.61.72.42.33.33.24.54.04.86.4

Preview Mode

This document has 7 pages. Sign in to access the full document!

Report

Study Now!

Document Details

Related Documents

Statistics - Univariate Inferential Tests

Statistics - Sampling

Statistics - Probability

Statistics - Principles of Testing

Statistics - Numerical Measures

Statistics - Introduction to Statistics

Statistics - Graphic Displays

Statistics - Cummulative Reviews

Statistics - Common Mistakes and Tables

Statistics - Bivariate Relationships

Company

Explore

Study Tools