10_week_2_session_2_final_copy_summ08

10_week_2_session_2_final_copy_summ08 - Statistics 10...

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Statistics 10 Professor: Esfandiari Week 2 Session 2 Summer 08 The objective of this part of this handout is to: Introduce you to scatterplots as a mean of displaying relationship between two quantitative variables. Show sample data and scatterplots that display perfect direct and inverse relationship Show you how linear transformation has no effect on the magnitude of correlation. Show you scatterplots that display direct and inverse relationships that are not perfect Introduce to you the coefficient of correlation as a mean of calculating the strength of relationship between two quantitative variables. Show that coefficient of correlation is equal for standardized and non- standardized data Discuss coefficient of correlation for non-linear data Explain the difference between correlation and causation Examples of perfect inverse and direct relationships From elementary science we know that Density = Mass/Volume or D = M/V This shows that when you keep volume constant, whatever change that you make in mass will be reflected in density. For example, if you multiply mass by two, density will also be multiplied by 2; given that volume stays constant. This is an example of a perfect and direct relationship. If you keep mass constant, whatever change that you make in volume, the inverse of that change will be made in density. For instance, when you keep mass constant, if you double the volume, density will be divided by two. This is an example of a perfect inverse relationship. The condition of perfect direct and inverse relationship is displayed by a sample data set 1
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given in table 1 and plots 1 and 2 Table 1: Density and mass keeping volume constant ( density = mass /volume ) density Mass volume 1 2 40 2 4 38 3 6 36 4 8 34 5 10 32 6 12 30 7 14 28 8 16 26 9 18 24 10 20 22 11 22 20 12 24 18 13 26 16 14 28 14 15 30 12 16 32 10 17 34 8 18 36 6 19 38 4 20 40 2 Plot 1: Perfect direct linear relationship between density and mass, keeping volume constant DENSITY 30 20 10 0 50 40 30 20 10 0 2
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Plot 2: Perfect inverse relationship between density and volume keeping mass constant VOLUME 50 40 30 20 10 0 50 40 30 20 10 0 Both in the case of plot 1 and plot 2, all of the points are on the line. This shows a perfect direct or inverse relationship. In the case of perfect direct relationship, the coefficient of correlation is equal to +1 and in the case of perfect inverse relationship the coefficient of correlation is equal to – 1. We show the coefficient of correlation between two variables (say X and Y) with r and its magnitude ranges from – 1 to + 1. This will be discussed in more detail later. r = coefficient of correlation -1 < = r < = + 1 When r = +1, that means for all of the cases in which X is above the mean, Y is also above the mean and for all of the cases in which X is below the mean, Y is also below the mean. In the table 1 the cases for which both X and Y are above the mean have been
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This note was uploaded on 08/15/2008 for the course STATS 10 taught by Professor Ioudina during the Summer '08 term at UCLA.

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10_week_2_session_2_final_copy_summ08 - Statistics 10...

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