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Descriptive Methods in Regression Data comes in pairs of quantitative variables. Given such paired data (bivariate data), we want to determine whether there is a relationship between the two quantitative variables and, if so, identify what the relationship is. Regression analysis allows us to identify an equation that best fits the data, and to predict values of one variable based on another variable.
The straight-line linear regression model is a means of relating one quantitative variable to another quantitative variable
A way of predicting the value of one variable from another. It is a hypothetical model of the relationship between two variables. The model used is a linear one. Therefore, we describe the relationship using the equation of a straight line.
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The goal is to be able to predict new values of Y based on values of X
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Regression line: Line whose equation is used for prediction Line that best describes the relationship between y, the dependent variable and x, the independent variable. Describing a Straight Line Linear equation: When the relationship between X and Y is linear Linear equation: Y = bX + a
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Linear regression builds on the equation for a straight line because the relationship between the two variables is assumed to be linear A straight line should yield the best “fit” of the data points in a scatterplot (a linear model)
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A researcher suspects that there is a relationship between the number of promises a political candidate makes and the number of promises that are fulfilled once the candidate is elected. He examines the track record of 10 politicians. Use spss to construct a regression equation that predicts the number of promises made and promises kept by politicians.
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Scatterplot To see if scores may be related construct a graph of the scores, called a scatterplot The variable labeled X is plotted on the horizontal axis (the abscissa) The Y variable is plotted on the vertical axis (the ordinate) The score of a subject on each of the two measures is indicated by one point on the scatterplot
Conclusions drawn from scatterplots are subjective. A more precise and objective method for detecting straight-line patterns is the linear correlation coefficient.
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The linear correlation coefficient r(often simply called the correlation coefficient) measures the strength of the linear relationship between the paired x and y values in a sample.
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Direction of relationship A correlation coefficient indicates the direction of the relationship by the positive or negative sign of the coefficient A positive r indicates A positive (direct)relationship between variables X and Y As the scores on variable X increase, the scores on variable Y tend to increase A negative r indicates A negative (inverse)relationship between variables X and Y As the scores on variable X increase, the scores on variable Y tend to decrease
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