Explanatory variable goes on the x axis to make the correct regression lineCorrelation wont be different but the regression line will be different depending on what variable goes on what axisR^2 has a range between 0 and 1: square of these values gets smaller and closer to zeroR has a range between -1 and 1R^2: is the proportion of the variance in the y variable that is explained by the x variable (look at slide 67)Slide 68: lots of spread in mpg and 77% of that spread is explained by the fact that the cars vary in weight and weight and mpg are related to each other. 23% of the variance is not accounted for.Relationship between height and weight: height is the explanatory variable because height explains weight but not 100%. Weight can be explained by other things other than height.Regression line- gives us predicted y value for every value of x. for any given value of x, we can predict what the y value should be (given by the equation of the line; plug in values)Predictions are imperfect, points will be scattered around the line both above and below itTrying to minimize the distance between the points and the linePrediction gives us a lot of the variance but there are residualsResiduals- unexplained parts of the y values (unpredicted values)  distance from point to the regression linePlotting the residuals directly  tend to be around zero  don't want to see a pattern in the residual graph. Want the residual plot to be scattered because if they’re scattered, the relationship between the variables is linearResidual plot where the variables are not linear  residual plot is shaped similarly to the original scatter plot. Not random scatter of residual plot = non linear relationship between variablesHeteroscedasticity- the variance of y is not the same across the levels of xSlide 73: Residual plot shows that the relationship between weight and price is strong when the weight is low but once the weight gets heavier, the relationship between weight and price is weakUse residuals to: Diagnose non linear relationships, diagnose heteroscedasticityDon't make inferences about the value of y for values of x that aren’t in the range  don't extrapolate outside of the range of observed x valuesRead over the terms on slide 76*direct, indirect, and common cause: often you don’t know what’s causing the correlation/relationship between the variables; requires researchindirect there’s a mediating causecorrelation doesn't imply causation but sometimes there is a causal relationship between the variablesto find the equation of the regression line: you need the correlation between the two variables (r value), the mean, and the standard deviation of each of the variables  plug them in and solve for the slope and interceptRelationships between quantitative variables 02/18/2014-Explanatory variable goes on the x axis to make the correct regression line-Correlation wont be different but the regression line will be different depending on what variable goes on what axis-R^2 has a range between 0 and 1: square of these values gets smaller and closer to zero-R has a range between -1 and 1-R^2: is the proportion of the variance in the y variable that is explained by the x variable (look at slide 67)-Slide 68: lots of spread in mpg and 77% of that spread is explained by thefact that the cars vary in weight and weight and mpg are related to each other. 23% of the variance is not accounted for. -Relationship between height and weight: height is the explanatory variable because height explains weight but not 100%. Weight can be explained by other things other than height.-Regression line- gives us predicted y value for every value of x. for any given value of x, we can predict what the y value should be (given by the equation of the line; plug in values)-Predictions are imperfect, points will be scattered around the line both above and below it-Trying to minimize the distance between the points and the line -Prediction gives us a lot of the variance but there are residuals-Residuals- unexplained parts of the y values (unpredicted values)  distance from point to the regression line-Plotting the residuals directly  tend to be around zero  don't want to see a pattern in the residual graph. Want the residual plot to be scattered because if they’re scattered, the relationship between the variables is linear-Residual plot where the variables are not linear  residual plot is shaped similarly to the original scatter plot. Not random scatter of residual plot = non linear relationship between variables -Heteroscedasticity- the variance of y is not the same across the levels of x-Slide 73: Residual plot shows that the relationship between weight and price is strong when the weight is low but once the weight gets heavier, the relationship between weight and price is weak-Use residuals to: Diagnose non linear relationships, diagnose heteroscedasticity -Don't make inferences about the value of y for values of x that aren’t in the range  don't extrapolate outside of the range of observed x values -Read over the terms on slide 76*-direct, indirect, and common cause: often you don’t know what’s causing the correlation/relationship between the variables; requires research-indirect there’s a mediating cause -correlation doesn't imply causation but sometimes there is a causal relationship between the variables -to find the equation of the regression line: you need the correlation between the two variables (r value), the mean, and the standard deviationof each of the variables  plug them in and solve for the slope and intercept