BNAD 276 Lecture Notes - Lecture 13: Simple Linear Regression, Madelyn Pugh, The Intercept
18 Mar 2017
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The correlation coefficient indicates both the direction and the strength of the linear relationship. A study in 2010 showed that consumers in 26 cities made debt payments from to per month. Economist madelyn davis believes that income differences are the main reason for the disparity. She is less sure about the impact of unemployment. She uses correlation analysis and regression analysis to learn more. We examined covariance and correlation as exploratory tools in chapters 2 & 3. Recall that covariance is a numerical measure that reveals the direction of the linear relationship between two variables. The sample covariance is computed as: (cid:3051)(cid:3052)= (cid:4666)(cid:3051) (cid:3051) (cid:4667)(cid:4666)(cid:3052) (cid:3052) (cid:4667) The sample correlation coefficient can be computed using: (cid:1870)(cid:3051)(cid:3052)= (cid:3046)(cid:3299)(cid:3300)(cid:3046)(cid:3299)(cid:3046)(cid:3300) For debt payments we have (cid:1877) =(cid:891)(cid:890)(cid:885). (cid:887) and sy= 124. 61. For income we have (cid:1876) =(cid:889)(cid:886). (cid:883) and sx=10. 35. We compute the covariance as: (cid:3051)(cid:3052)= (cid:4666)(cid:3051) (cid:3051) (cid:4667)(cid:4666)(cid:3052) (cid:3052) (cid:4667) (cid:2870)(cid:2874) (cid:2869) =(cid:883)(cid:883)(cid:883)(cid:891). (cid:883)(cid:890)
