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 Measure of association A general term that refers toa number of bivariate statistical techniques used to measure the strength of a relationship between two variables correlation coefficient a statistical measure of the covariation, or association, between two at least interval variables covariance extent to which two variables are associated systematically with each other Negative (inverse) relationship Covariation in which the association between variables is in the opposite direciton. As one goes up, the other goes down Does covariation in and of itself establish causality? No. Think of the example of the covariation between ice cream sales and drownings; or the roosters crow and the rising sun Coefficient of Determination (R^2) A measure obtained by squaring the correlation coefficient; the proporion of the total variance of a variable accounted for by another value of another value. Measures that part of the variance of Y that is accounted for by knowing the value of X In the example about unemployment and hours worked, r = -.635; therefore r^2=0.403 How much of the variance in unemployment can be explained by the variance in hours worked? About 40% of the variance in unemployment can be explained by the variance in hours worked. Correlation Matrix The standard form for reporting observed correlations among multiple variables. Although any number of variables can be displayed in a correlation matrix, each entry represents the bivariate relationship between a pair of variables. What is the procedure for determining statistical significance? The procedure for determining statistical significance is the t-test of the significance of a correlation coefficient Simple (Bivariate) Linear Regression A measure of linear association that investigates straight line relationships between a continuous dependent variable and an independent variable that is usually continuous, but can be a categorical dummy variable In simple linear regression, what do the following symbols stand for: Y (alpha) (beta) X (Y = (alpha) + (beta)X (alpha) represents the Y intercept, or where the line crosses the y-axis (beta) is the slope coefficient The slope is the change in Y associated with a change of one unit in X. Slope may also be thought of as rise over run. True/False: Beta provides the strength and direction of the relationship between the independent and dependent variable True True/False: (alpha) Y intercept is a fixed point that is considered a constant True Standardized regression coefficient Estimated coefficient of the strength of relationship between the independent and dependent variables Expressed on a standardized scale where higher absolute values indicate stronger relationships (between -1 to 1) Raw Regression Estimates (b1) Raw regression weights have theadvantage of retaining the scale metric (also their key disadvantage). Used if the purpose of the regression analysis is forecasting. Standard Regression estimates ((Beta)1) Have the advantage of a constant scale. Should be used when the research is testing explanatory hypothesis Ordinary Least Squares Generates a straight line that minimizes the sum of squared deviations of the actual values from this predicted regression line. The equation for the ordinary least squares means that X estimated how? The equation menas that the predicted value for any value of X is determined as a funciton of the estimated slope coefficient, plus the estimated intercept coefficient + some error Where does the explanatory power of regression lie? The explanatory power of regression lies in hypothesis testing What two conditions must be satisfied for the outcome of the ypothesis test? The regression weight must be in the hypothesized direction. (positivie relationships require a positive coefficient and negative relationships require a negative one) The t-test associated with the regression weight must be significant Multiple Regression Analysis An analysis of association in which the effects of two or more independent variables on a single, intervalscaled dependent variable are investigated simultaneously Dummy Variable The way a dichotomous (two group) independent variable is represnted in regression analysis by assigning 0 to one group and 1 to another Partial correlation The correlation between two variables after taking into account the fact that they are correlated with other variables too R^2 in multiple Regression The coefficient of multiple determination in multiple regression indicates the percentage of variation in Y explained by all independent variables F-Test Tests statistical significance by comparing the variation explained by the regression equation to the residual error variation . Allows for testing of the relative magnitudes of the sum of squares due to the regression and the error sum of squares