Statistics midterm(hw1) Questions & Answers

Statistics Chapter 3 Questions & Answers (xbar, y bar) - ANSWER: The least-squares regression line for any data set passes through the point (x bar, y bar) 2 tools to describe the relationship between variables - ANSWER: 1.) Correlation 2.) Regression Accuracy of predictions - ANSWER: The accuracy of predictions from a regression line depends on how much the data scatter about the line. Another meaning of correlation - ANSWER: The average of the products of the standardized scores Another name for residual - ANSWER: Prediction error Are all outliers influential? - ANSWER: The least-squares line is most likely to be heavily influenced by observations that are outliers in x. Influential points often have small residuals because they pull the regression line toward themselves. The scatterplot alerts you of these (don't just plot residual plot b/c may miss influential points) Association does not imply causation - ANSWER: An association between an explanatory variable x and a response variable y, even if it is very strong, is not by itself good evidence that changes in x actually cause changes in y. *Sometimes association is due to cause and effect but other times it is due to lurking variables Benefits of residuals - ANSWER: Residuals show how far data fall from regression line and thus help us assess how well the line fits/describes the data. Residuals can be be calculated from any model fitted to data. However, residuals from least-squares line have a special property: the mean of the least-squares residuals is always zero. Causation - ANSWER: Often we want to know whether changes in the explanatory variable causes a change in the response variable. Remember, correlation does NOT imply causation. Caution w/ scatterplots - ANSWER: Association does not imply causation because there may be other variables lurking in the background that contribute to the relationship between two variables