UASTAT151Ch3 - Ch 3 Intro to Correlation and Regression Ch 2 deals with univariate data This chapter however considers bivariate data and how two

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Ch. 3 – Intro to Correlation and Regression Ch. 2 deals with univariate data. This chapter, however, considers bivariate data and how two numerical variables are related. Methods of description are introduced here and formalized in Ch. 11. Terminology : x y Explanatory variable Response variable Independent variable Dependent variable Predictor variable Predicted variable Notation : - bivariate sample of size n : { ( x 1 , y 1 ), ( x 2 , y 2 ), …, ( x n , y n ) } - sample means: x , y - sample std dev.: s x , s y Displaying relationships : Def’n: An association exists between two variables if a particular value for one variable is more likely to occur with certain values of the other variable. A scatterplot is a graphical display of two quantitative variables. - x -variable goes on the x -axis, y -variable on the y -axis - origin (0,0) may be included Look for : - form of relationship (i.e. any obvious pattern) - strength of relationship (i.e. closeness of fitting to a line) - direction of relationship (i.e. positive or negative association) - any unusual observations or outliers x y 1 1 2 2 4 1 3 2 (graph of above data used to discuss scatterplot traits further) Correlation : Def’n: Pearson’s Sample Correlation Coefficient r is given by r = = = i i y x n i y i x i z z n s y y s x x n 1 1 1 1 1 where i x z is the “standardized” observation for x i and i y z is the “standardized” observation for y i for i = 1, …, n (example graphs of correlation drawn in class: 1. strong positive linear; 2. weak positive linear; 3. strong negative linear; 4. no pattern; 5. parabola; 6. exponential)
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Properties of r :
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This note was uploaded on 07/31/2011 for the course STAT 151 taught by Professor Henrykkolacz during the Winter '07 term at University of Alberta.

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UASTAT151Ch3 - Ch 3 Intro to Correlation and Regression Ch 2 deals with univariate data This chapter however considers bivariate data and how two

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