Stack #75166
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| independent variable x is | called the explanatory variable
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| dependent varaible y is called | the response variable
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| scatterplots are usually analyzed according to | direction, form, strenth, and outliers
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| direction is | whether there isa positive assocaition, engative association or neither
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| form | clusters of points, linear patter
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| strength of the relationship | how close to a straight line do these points appear to lie
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| outliers | points that do not follow the gernal pattern of the data
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| correlation coeffiicent | measures the direction and strength of the linear relationship between two quanittiative varaibles
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| formula for r | i/n-1 times sigma xi-x ove sx times yi-y over sy
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| correlation coefficient r is always a number between and including | -1 and 1
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| if r is positive then x and y are said to have a | positive assocaiting
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| if r=1 then x and y have a | perfect positive correlatrion
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| if r is negative then x and y have a | negative assocaition
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| if r= -1 then x and y have a | perfect negative correlationsghip
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| the closer r is to either 1 or -1 | the stronger the relationship is between the two variables
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| if r=o | there is no correlation between the two variables
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| teh correlation coefficent only measures | the existence and strength of linear relationships
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| the formula for the correlation coefficient is extremely | sensitive to outliers
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| the correalation coefficient has | no units
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| the corrleation coefficient is the same | regardless of which variable you consider to be the explanatory and which you consider to be the response
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| formula for lsqr | y hat equals naugth plus b1x
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| b1 is the | slope of the line
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| b1 formula is | r sy/sx
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| naught is | the y intercept of the line
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| banaught formula is | ybar minus b1xbar
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| teh diference btween y and yhat is caled | an error or a residual
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| a residual is | the observed value of y minus the prediceted value of y
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| the point xbar and ybar is a pooint | on every regression line
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| fsquared is called the | coefficient of determination and meaures the variation in y that is explained by y's linear assocaition with x
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| a residual plot | graphs the residuals on the vertical axis adn either the explanatory response or rpredicted response values on the horizontal acis.
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| residuals from a LSQR alwasy ahve a mean of | 0
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| the horizontal axis | of a residual plot correspond to the regression line, which means trhat a residual point plotted onm the horizontal axis has a residual value of 0
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| the correlation coefficient and the lsqr for a set of data | can be strongly influence by an outlying observation
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| an observation is influiential if | removing it would markedly change the position fo the rergression line
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| if the ordered pairs x,y ina d ata set dispalay a graph with an approxiamately exponetial shape then the graph of the ordred paris | x, log y will display a graph owith an approximately linear shape
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| if the ordered pairs x, y ina d ata set display a graph tyhat is approximately a power function then the graph of the ordered pairs | log x, log y will display a graph with an approxialmatley linear shape
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| if a function resembles a power function then it is reasonable hat the point | 0,0 should lieo n its graph
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| extrapolation is the | use of a regression line for prediction ioutside the range of balues of the explanatory variable x that yo used to obtain the line such predictions cannot be trusted
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| interpolation is the use | ogf a repgression line for a rpediction inside the range of the values of x, making it a more trustworthy procedure
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| association does not imply casuation | in othjer wrods, a strong correlation between two varaibles does not mean that a cause adn effect relationsip exists between them
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| a lurking variable is a variable that has | an important effecton the relationshi among the varibles in a study but is not included among the varaibles
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| a confounding varaible is a | lurking vatriable that affects only he response variable but creates a situation here it is impossible to dete4rmine whether ther affect on the respmse variable is caused by the explanatory variable, the confusing lurking variable, or neither
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lilee256