Lecture Notes Regression Chapter 14 – Regression Analysis: Use of a relationship between X-Y pairs to explain or predict variation in Y in terms of differences in the X’s. Prediction: Use of a relationship between X-Y pairs to predict values of Y based on knowledge of X. For example, since I know that your high school GPA was 3.7, I predict that your college GPA will be about 3.1. Regression Sample A sample for which you have X-Y pairs with no missing members of either pair. Used it to develop a prediction equation, a simple equation relating predicted Ys to Xs. The prediction equation Predicted Y = Additive constant + multiplicative constant * X. Predicted Y = a + bX We’ll use this: Predicted Y = a + bX = or equivalently, bX + a The second version, bX+a is best for use when you’re doing hand computations. Regression line The prediction equation forms a straight line on the scatterplot of Y vs. X. That line is called the regression line or line of best fit. b and a and the regression line The constant, b, is the slope of the regression line on a scatterplot. The constant, a, is the y-intercept of the line. Prediction from the equation For persons for whom you have X but not Y, simply plug their X value into the equation (assuming you’ve obtained values of a and b) to generate the predicted Y for each one. Why do regression analysis? 1. Economy in prediction. If you have 1000’s of Xs, it would be very difficult to examine all of them to obtain a predicted value for someone. But with the equation, it’s easy. 2. Theory. It may be of theoretical interest to know that there is a relationship between Ys and Xs that is expressed by the simple equation: Predicted Y = a + bX. 3. Objectivity in prediction. Without the equation, we might argue about what the predicted Y should be for a person. With it, we all get the same number.
Lecture Notes Regression – Chapter 14 Regression Analysis: Use of a relationship between X-Y pairs to explain or predict variation in Y in terms of differences in the X’s. Prediction: Use of a relationship between X-Y pairs to predict values of Y based on knowledge of X. For example, since I know that your high school GPA was 3.7, I predict that your college GPA will be about 3.1. Regression Sample A sample for which you have X-Y pairs with no missing members of either pair. Used it to develop a prediction equation, a simple equation relating predicted Ys to Xs. The prediction equation Predicted Y = Additive constant + multiplicative constant * X. Predicted Y = a + bX We’ll use this: Predicted Y = a + bX = or equivalently, bX + a The second version, bX+a is best for use when you’re doing hand computations. Regression line The prediction equation forms a straight line on the scatterplot of Y vs. X. That line is called the regression line or line of best fit. b and a and the regression line The constant, b, is the slope of the regression line on a scatterplot. The constant, a, is the y-intercept of the line. Prediction from the equation For persons for whom you have X but not Y, simply plug their X value into the equation (assuming you’ve obtained values of a and b) to generate the predicted Y for each one. Why do regression analysis? 1. Economy in prediction. If you have 1000’s of Xs, it would be very difficult to examine all of them to obtain a predicted value for someone. But with the equation, it’s easy. 2. Theory. It may be of theoretical interest to know that there is a relationship between Ys and Xs that is expressed by the simple equation: Predicted Y = a + bX. 3. Objectivity in prediction. Without the equation, we might argue about what the predicted Y should be for a person. With it, we all get the same number.
p2010_lecture16_regression.docx