what are we interested in when exploring bivariate data
whether not/how changes in one variable can allow us to predict changes in the other variable
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scatterplot
2-dimensional graph of ordered pairs
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what do we say about positively associated variables
higher than average values of one variable TEND TO BE PAIRED WITH higher than average values of the other variable
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correlation coefficient (r) is a measure of what?
the strength of the LINEAR relationship between 2 variables, as well as the direction of this relationship (+ or -)
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if r is equal to the absolute value of 1ā¦
all points lie on a line
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if abs(r) is greater than .8ā¦
the LINEAR correlation is generally regarded to be strong
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if abs(r) is between .5 & .8ā¦
the LINEAR correlation is generally regarded to be moderateif
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if abs(r) is less than .5ā¦
the LINEAR correlation is generally regarded to be weak
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if r is = 0, there isā¦
no LINEAR correlation (may be nonlinear correlation)
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if you change the order of the explanatory/dependent variables, what effect will this change have on r?
none!
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if you change the units of measurement of one of your variables (e.g. ft to yrds), what effect will this change have on r?
none!
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is r resistant to extreme values? why/why not?
no; r is based on the MEAN & is effected by extreme values
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least squares regression line does what?
minimizes the sum of squared errors/distances of points from our line
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residual
difference between the observed values of the response variable (y) and the predicted values (Å·) from the model
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a negative residual means that Å· was tooā¦
large
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a positive residual means that Å· was tooā¦
small
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a pattern of residuals that doesnāt appear to be randomly distributed about 0 indicatesā¦
a regression line that isnāt a good model of our data
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interpolation
trying to predict a value of y from a value of x which is WITHIN the range of x-values we have (your traditional prediction, think internal)
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extrapolation
trying to predict a value of y from a value of x which ISNāT within the range of x-values we have (unadvised, rarely have confidence, think external)
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coefficient of determination
r^2; the proportion of the total variability in y which is explained by the regression of y on x
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outlier when dealing with bivariate dataā¦
lies outside the general pattern of data (for regression, datapoint has a LARGE RESIDUAL)
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influential observation
an observation that has a strong influence on the regression model; most influential points tend to be extreme in the x direction (high LEVERAGE points)
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