Week 8: Chapters 14 & 15
Week 8: Chapters 14 & 15 STAT 1350 Intro to Stats
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This 3 page Class Notes was uploaded by Katie Catipon on Tuesday February 24, 2015. The Class Notes belongs to STAT 1350 Intro to Stats at Ohio State University taught by Alice Miller in Spring2015. Since its upload, it has received 104 views. For similar materials see Intro to Stats in Statistics at Ohio State University.
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Date Created: 02/24/15
Chapter 14 Describing Relationships Scatterplots and Correlation Scatterplots the most common way to display the relationship between two quantitative variables measured on the same individuals Each individual in the study appears as a point in the plot The point is determined by both variables for that one individual How to examine a scatterplot look for the overall pattern described by form direction and strength and striking deviations from the pattern outliers Positive association Values correlate in that aboveaverage values of one variable accompany aboveaverage values of the other variable and belowaverage values of variables do the same The slope moves upwards from left to right Negative association Aboveaverage variable values accompany belowaverage variable values Plot slopes downward left to right Form general shape of the graph Strength determined by how closely points follow a clear form Straightline relations simple and common It is strong if the points all lie close to the line and weak if they are widely scattered about the line Correlation r measure that describes the direction and strength of a straightline relationshipquot 1 if The symbol 2 called sigma means add them all up w ug xthsrliw r positive association 0 r negative association 0 ralways falls between 1 and 1 Near 0 indicate weak straightline relationship r 1 or 1 only occur when the points lie exactly on the straight line 0 Correlation is not affected by a change in units of measurement 0 Correlation ignores distinction between variables changing which is labeled xand ydoes not affect it 0 Correlation is strongly affected by outliers Chapter 15 Describing Relationships Regression Prediction and Causation Prediction Fits a model to a set of data works best when the model ts the data closely l prediction outside the range of data extrapolation and leads to false predictions Regression line a straight line that describes how a response variable ychanges with the explanatory variable X Often used to predict the value of yfor given value of X Leastsquares regression line the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible Regression in terms of correlation Correlation measures direction amp strength of a straightline relationship Regression draws line to describe this relationship 0 Both are strongly affected by outliers Usefulness of regression line for prediction depends on strength of association aka correlation between the variables 0 The square of correlation rquot2 proportion of the variation in values of ythat is explained by the least squares regression of yon X l when reporting regression usually give rquot2 as measure of successfulness of regression as an explanation of the response Causation Strong relationships between variables does not necessitate a causeeffect relationship 0 Relationships between variables are often in uenced by lurking variables 0 Best evidence of causation comes from randomized comparative experiments 0 Even when direct causation is present it is rarely the complete explanation for the variables relationship 0 Three types of causation note two or more of these may happen simultaneously 0 Direct causation 0 Common response 0 Confounding Observed relationships can be used to make predictions without worry of causation as long as the patterns continue to hold true in data 0 Establishing causation without an experiment Criteria O 00 Association between variables is strong Association is consistent throughout many studies reduces effects of lurking variables Higher doses l stronger responses Alleged cause comes before effect chronologically Alleged cause is plausible
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