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Deterministic relationships |
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-every x has a y value -linear and non-linear |
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y = a + b( x ) a = intercept b = slope |
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Probabilistic relationship |
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-when there are (possibly) many of y for each x -linear or non-linear ex. there are many weights for the height 5'7" height = x weight = y |
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Conditional distributions |
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the distribution of y values ex. weight for "height and weight" because weight is conditional to height |
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as x increases, y increases |
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as x increases, y decreases |
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a measure of the strength of linear association between two variables; strength is represented by how tightly clustered the points are to an imaginary like that runs through the scatterplot; represented by r |
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Finding correlation coefficient |
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1. turn all data points into z-scores 2. multiply Zx by Zy for each pair 3. sum the products of all 4. divide by n - 1 |
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all of the conditional distributions have the standard deviation as one another |
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Bivariate normal distribution |
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-both x and y distribution are normal distributions (marginal distributions) -for each value of x, there is a distribution of y values -as x increases linearly, y values change linearly -each conditional distribution is a normal distribution -all conditional distributions have the standard deviation |
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distribution of x and y variables in a bivariate normal distribution; x-scores and y-scores (according to mean and standard deviation) are normal distributions |
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depends on p and sample size (n) |
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meaning that the correlation between two variables is high because of a third-party variable. |
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