Correlation & Regression – Flashcards
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What information is provided by the sign (+ or -) of the Pearson correlation?
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A positive correlation indicates that X and Y change in the same direction. As X increases, Y also increases. A negative correlation indicates that X and Y tend to change in opposite directions: As X increases, Y decreases.
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What information is provided by the numerical value of the Pearson correlation?
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how well the data points fit a straight line. A value of 1.00 (or -1.00) indicates a perfect linear git and a value of zero indicates no linear trend.
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Does a correlation have an INDEPENDENT Variable?
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NO!
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What does a correlation do?
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It measures and describes a relationship between two variables by: DIRECTION (neg or pos), FORM, (linear is most common) STRENGTH.
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Perfect Linear Relationship
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1) every change in X has a corresponding change in Y; 2) Correlation will be -1.00 or +1.00.
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No Relationship
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X and Y do not covary; correlation will be 0
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Null Hypothesis
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p=0
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Alternative Hypothesis
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Non-directional p does not =0; Directional p>0, p<0
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Coefficient of Determination
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r^2; proportion of variability in one variable that can be determined from the relationship with the other variable.
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What are some issues of correlation?
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The effect of variability, outliers, range of data, ceiling effects, floor effects
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Spearman Correlation
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If you have ordinal data use when: 1. both variables are measured on an ordinal scale; 2. relationship is consistently directional but may not be linear
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Pearson Correlation
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measures a linear relationship between 2 variables
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Regression used to...
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1. predict the value of a dependent variable based on the values of at least one independent variable 2. explain the impact of changes in an independent
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Why is regression useful?
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1. makes the relationship easier to see; 2. shows the central tendency of the relationship; 3. can be use for prediction
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How many independent variables does a simple regression model show?
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1
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What is described by a linear function?
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relationship between x & y
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In simple regression what changes are assumed?
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changes in y are assumed to be caused by changes in x
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Regression Line
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line in regression: a method for determining the best-fitting line through a set of data
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What does the regression line do?
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minimizes the sum of the squared differences between the points & the line
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What is the difference between a point and the line of regression called?
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residuals or errors
