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# Stats 3000 Week 2 - Winter 2011

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### Stats 3000 Week 2 - Winter 2011

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2. 2. Descriptive Methods in <br />Regression <br />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. <br />Regression analysis allows us to identify an equation that best fits the data, and to predict values of one variable based on another variable. <br />
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4. 4. What is Linear Regression?<br /><ul><li>The straight-line linear regression model is a means of relating one quantitative variable to another quantitative variable</li></ul>A way of predicting the value of one variable from another.<br />It is a hypothetical model of the relationship between two variables.<br />The model used is a linear one.<br />Therefore, we describe the relationship using the equation of a straight line.<br />
5. 5. The goal is to be able to predict new values of Y based on values of X<br />
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9. 9. Regression line: Line whose equation is used for prediction<br />Line that best describes the relationship between y, the dependent variable and x, the independent variable.<br />Describing a Straight Line<br />Linear equation: When the relationship between X and Y is linear<br /> Linear equation: Y = bX + a<br />
10. 10. Linear regression builds on the equation for a straight line because the relationship between the two variables is assumed to be linear<br />A straight line should yield the best “fit” of the data points in a scatterplot (a linear model) <br />
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15. 15. Intercepts and Slopes<br />
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17. 17. Residuals - the difference between a score and its predicted value<br />
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24. 24. A researcher suspects that there is a relationship between the number of promises<br />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.<br />
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30. 30. slope<br />The information in the column “unstandardized coefficients” column B embodies the regression equation: (constant) is the intercept<br />
31. 31. <ul><li>Standard error of estimate: a measure of the error in prediction used as the basis for a measure of the accuracy of prediction</li></li></ul><li>
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35. 35. Scatterplot<br />To see if scores may be related construct a graph of the scores, called a scatterplot<br />The variable labeled X is plotted on the horizontal axis (the abscissa)<br />The Y variable is plotted on the vertical axis (the ordinate)<br />The score of a subject on each of the two measures is indicated by one point on the scatterplot<br />
36. 36. <ul><li>Conclusions drawn from scatterplots are subjective. A more precise and objective method for detecting straight-line patterns is the linear correlation coefficient.
37. 37. 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. </li></li></ul><li>Descriptive Methods in <br />Correlation <br />
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39. 39. <ul><li>The value of r is not affected by the choice of x or y. Interchange all x and y values and the value of r will not change.
40. 40. r measures the strength of a linear relationship. It is not designed to measure the strength of a relationship that is not linear.</li></li></ul><li>
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49. 49. Direction of relationship<br />A correlation coefficient indicates the direction of the relationship by the positive or negative sign of the coefficient <br />A positive r indicates<br />A positive (direct)relationship between variables X and Y<br />As the scores on variable X increase, the scores on variable Y tend to increase<br />A negative r indicates<br />A negative (inverse)relationship between variables X and Y<br />As the scores on variable X increase, the scores on variable Y tend to decrease<br />
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63. 63. SPSS assignment # 2 due next week<br />