CHAPTER 2 OUTLINE Studying Relationships When examining information for all states simultaneously scatterplots and correlation coefficients are superior to maps I THINK I M ASKING THIS IN CLASS FRIDAY 1 Variables attributes and characteristics that take on different values across the states ex population income education 2 Constants Descriptors that have identical values for all states 3 Outliers Data that is way far off from the regression line 4 Regression Line Determined by a statistical formula expressed by an algebraic equation and also determines the strength of a relationship Above the regression line means higher than predicted Below the regression line means lower than predicted 5 We are interested in in relationships between state variables 6 Something that is the same for all states can t be the cause of something that is different for all states and vise versa Patterns of Relationships between Variables 1 Direction First element of interest Positive When one variable goes up the other goes up ex of population with Bachelor s degrees and Per Capita income o Regression line will go from the lower left up to the upper right of the graph Negative When one variable goes up the other goes down ex Infant mortality rates and life expectancy o Regression line will go from the upper left down to the right Regression line will go from the lower left up to the upper right of the graph 2 Strength Second element of interest Correlation Technique for expressing relationships in quantitative terms This is represented by r ranging from 0 1 and 1 0 and indicates how well the regression line fits the scatterplot elements o No relationship at all is 00 or 00 The regression line for no relationship would be either vertical or horizontal 00 to 29 and 29 to 00 are so weak that there is no relationship as well o Weak relationships range from 0 3 to 0 4 o Moderate relationships range from 0 5 to 0 6 o Strong relationships range from 0 7 Be very wary when you see a correlation that is 8 and 9 as relationships can t be that strong in social science This means that that the relationship is random happened by chance 3 Empirical Relationships Relationships that are data driven and proven by scientific measurement Also how things associate in the real world Can also exist when variables we correlate are both strongly related to a third variable or multiple variables other than the two already calculated for a relationship 4 Casual relationships Cause and effect One can sometimes deduce relationship based on prior knowledge and studies education Education causes higher per capita income vs high per capita income causing 5 Spurious relationships Correlation is either an extremely strong and positive negative Be careful if you see a correlation of 0 8 0 9 the relationship can t be that high in social sciences High correlation implies that the relationship was by chance or was random Ex When there are more fire engines at a fire there is more damage Severity of the fire causes both the number of fire engines responding and the extent of damage o When population size is ignored and all measures used to determine a relationship are based on population size the graphs will be bad because the highest populated states will always rank at the top of the regression line and the smaller states will cluster at the bottom
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