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what are the two purposes of the pearson correlation and regression descriptive aspects: to study the relationship between __ and to predict scores on one variable from scores of __- how are scores __
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use X for the __ (__) variable and Y for the __ (__) variable
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chap 5 stats
| Question | Answer |
|---|---|
| what are the two purposes of the pearson correlation and regression descriptive aspects: to study the relationship between __ and to predict scores on one variable from scores of __- how are scores __ | interval level variables, another variable, how are scores related to one another |
| use X for the __ (__) variable and Y for the __ (__) variable | predictor (independent), criterion (dependent) |
| the pearson correlation is used to determine the extent to which .. | two variables approximate a linear relationship |
| regression is used to identify the line that best describes this relationship as determined by a statistical criterion known as the | least squares |
| the relationship between certain variables X and Y, represents the values of X on the abscissa and the values of Y on the ordinate, and the scors for each individual on the body of the graph | scatterplot |
| indicates the number of units that variable Y changes as variable X changes by one unit | slope |
| the slope (B)= (state equation) | y1-y2/ x1-x2 |
| a relas X increases so does Y and as X decreases so does Y- this shows what relationship | positive |
| inverse relationship between x and y varialbes is what relationship | negative |
| point at which a line intersects the y axis when x=0 | intercept |
| intercept denoted by letter | a |
| a linear model is a __ that states the __ relationships and how they can differ in the values of their __ and values of their __ | equation, linear, intercepts, slopes |
| linear model equation | y=a+bX |
| b= the __ and a= the __ | slope, intercept |
| in the intercept the line intersects the __ axis and _=0 | y, x |
| using the linear equation we can substitute the scores on __ and get the scored predicted on __ | x, y |
| the pearson correlation coefficient can range from __ to __ and is represented as _ | -1.00 to +1.00, r |
| the sign of the correlation coefficient indicates the __ of linear approximation (+) means __ and (-) means __ | direction, direct relationship, inverse relationship |
| correlation coefficient of 0 means that there is | no linear relationship between the 2 relationships |
| the magnitude of the correlation coefficient is indexed by its | absolute value |
| the magnitude indicates the __ to which a __ is approximated | degree , linear relationship |
| the further r is in either a positive or negative direction from 0, the ... | higher the magnitude |
| we can use the __ of the __ of z scores as an index of the relationship between two variables | sum, products |
| the sum of the products of z scores can be influences by __ and __ | size of correlation and sample size |
| how do you fix this problem? | divide by N |
| we divide by N in order to have an index of correlation independent of __ and because dividing by N will always make .. | N, scores fall between -1 and +1 |
| what is SSx and SSy | sum of squares for variable X and variable Y |
| sum of crossproducts is more precise and efficient because it requires __ and presents __ | fewer steps, presents fewer opportunities for rounding error |
| the fact that two variables are correlated does not necessarily imply that one variable __ the other to vary as it does, it is possible for two varailbes to be related to one another but have no __ | causes, causal relationship |
| the meaning of a certain correlation coefficient __ within the study | varies |
| in behavioral science research, correlations of __, __ and __ __ are considered significant | +/- .20 +/- .30 |
| the proportion of variability in the dependent variable that can be explained by or that is associated with the independent variable | coefficient of determination (r2) |
| the proportion of variability in the dependent variable and cant be explained by and is not associated with the dependent variable | 1-r2 |
| when two variables are not perfectly correlated, the statistical technique of __ can be used to identify a line that fits the data points better than any other line | regression |
| regression is determined by the | least squares criterion |
| the regression line describes the nature of the __ between the two variables | linear relationship |
| the linear relationship beetween 2 varialbes can be represented by a regression line that takes the general form of | y=a +bx |
| the slope of the regression line equation: | b=SCP/SSx |
| intercept regression line equation | a=y-bX |
| the regression line is the line that __ the __ at the value of the | intersects the yaxis at the value of the intercept |
| and the slope of this line is scuh that when x increases by one unit, | y increases by the b |
| the slope and the intercept are defined so as to minimize the ___ that the data points are from the regression line | squared vertical distances |
| the criterion for deriving the values of the slope and intercept | least squares criterion |
| the least squares criterion concerns itself with the squares of the __ and formally defines the values of the slope and intercept so as to __ the __ | discrepancy scores, minimize the sum of these squared errors |
| the amount of error for a given individual can be represented by the discrepancy between that persons __ and __ _ scores | actual and predicted y scores |
| least squares criterion is limited by the fact that the sum of the discrepancies between the actual y scores and y scores predicted from the regression equation will.. | always equal zerio |
| index of predictive error | standard error of estimate |
| typical error made when predicting y from x | standard error of estimate |
| conditions of standard error of estimate (4) | x and y are interval level measurements, same individuals are measured on both x and y, there is a linear trend between x and y predictions shouldnt be made with scores on x beyond the range measured |
| x and y in Syx are __ measurements | interval |
| same individuals are measured on | both x and y |
| there is a __ trend between x and y | linear |
| predictions shouldnt be made withs cores on __ beyond the range measured | x |
| absolute magnitude of the standard error of estimate is | meaningful |
| the standard error of estimate can be compared with the __ of Y which indicated what the average error in prediction would be if one were to predict a Y score equal to the mean of Y for each individual | standard deviation |
| if two variables are related in a nonlinear way the pearson correlation will | not be sensitive to this |
| if they are related nonlinearly what are effective models | curvilinear or polynomial regression |
| the regression equation for predicting variable x from varialbe y is not the same as the regression equation for predicting variable _ from variable x | y, x |
| example of this | conversion rates |
| from a statistical perspective, the designation of one variable as X and one varialbe as Y is | arbitrary |
| the use of __ presupposes an underylying rationale for making predictions about variable y from variable x, | regression |
| if interest is merely in whether a given variable is linearly related to another __ can be applied | pearson correlation |
| from a conceptual perspective the decision of which variable to designate as X and which to designate as Y has | important implications |
| depending on the particular circumstances, the __ of the correlation when a limited portion of this range is considered might be either less than or greater than if the range had not been so restricted | magnitude |
| if two variables are linearly related, then restricting the range of one variable will __ the __ of the __ | reduce the magnitude of the correlation coefficient |
| prediction of y from x is only meaningul for the _ of __ values that formed at the basis for the calcuation of the __ equation | range of x, regression |
| we must not extend our interpretation of correlational results outside the range of the original data set- the conclusions drawn from a correlational analysis apply only to the | range of variables on which the correlation was based |
| the pearson correlation coefficient reps the extent to which two variables approximate a linear relationship for the __ of __ included in its __ | range of variables, calculation |
| when using the regression equation for standard scores.. first __ the x and y scores and then apply the __ to calculate the __ for the regression line based on standard scores | standardize x and y scores, apply formula to calculate slope |
| in regression line eq. you dont have to calculate the intercept of the regression line when standard scores are analyzed in this manner because it will always | equal zero |
| the slope of the regression line in this instance will always equal the | correlation ccoefficient |
| a correlation coefficient conveys the number of __ that one variable is predicted to change given a change of one standard score in the other variable, other things being __ | standard scores, equal |
| the magnitude and sign of a correlation coefficient can be influenced by __ | outliers |
| outliers can do what? | turn weak correlation into strong or strong correlation into weak |
| how strong a relationship is determined through | r^2=SSexplained/SStotal |
| correlation coeff R (2) | nature of relationship, strength of relationship |
| why would we standardize the slope | slope of regression line should be 0 when no linear relationship |
| nature of linear relationship is determined by the sign of | b or r |
| coef of determination indicates proportion of __ in _ explained or predicted by _ | variability, y, x, |
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lilcollins92