Introduction to Linear Regression and Correlation Analysis参考.ppt

Chapter 13Introduction to Linear Regression and Correlation Analysis Chapter Goals After completing this chapter, you should be able to: Calculate and interpret the simple correlation between two variables Determine whether the correlation is significant Calculate and interpret the simple linear regression equation for a set of data Understand the assumptions behind regression analysis Determine whether a regression model is significant Chapter Goals After completing this chapter, you should be able to: Calculate and interpret confidence intervals for the regression coefficients Recognize regression analysis applications for purposes of prediction and description Recognize some potential problems if regression analysis is used incorrectly Recognize nonlinear relationships between two variables Scatter Plots and Correlation A scatter plot (or scatter diagram) is used to show the relationship between two variables Correlation analysis is used to measure strength of the association (linear relationship) between two variables Only concerned with strength of the relationship No causal effect is implied Scatter Plot Examples Scatter Plot Examples Scatter Plot Examples Correlation Coefficient The population correlation coefficient ρ (rho) measures the strength of the association between the variables The sample correlation coefficient r is an estimate of ρ and is used to measure the strength of the linear relationship in the sample observations Features of ρ and r Unit free Range between -1 and 1 The closer to -1, the stronger the negative linear relationship The closer to 1, the stronger the positive linear relationship The closer to 0, the weaker the linear relationship Examples of Approximate r Values Calculating the Correlation Coefficient Calculation Example Calculation Example Excel Output Significance Test for Correlation Hypotheses H0: ρ = 0 (no correlation) HA: ρ ≠ 0 (correlation exists) Test statistic (with n – 2 degrees of fr