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2201 Final Review

2201 Final Review - Click to edit Master subtitle style...

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Click to edit Master subtitle style 5/20/10 2201 Final Review

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5/20/10 Simple Linear Regression Correlation: Used to assess the strength of the linear relationship between two numerical variables Regression: Used to estimate the linear relationship between two variables, and then use that to predict Descriptive: uses least squares to estimate relationship
5/20/10 Simple Linear Regression -Descriptive With descriptive: no assumptions being made Y i = β o + β 1 X 1 Y i : is the ith response associated with xi β o is the y intercept, value when x=0 Β 1: is the slope

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5/20/10 Simple Linear Regression -Descriptive Y i hat Ӯ (xi, yi) Yi-Yi hat Yi hat - Ӯ The whole point: (Yi-Yi hat)^2 + (Yi hat – Σ Σ Ӯ )^2 = (Yi – Σ )^2 Ӯ SSE + SSR = SSTo
5/20/10 Simple Linear Regression – Descriptive Observ X: ATM Disbur. (\$1000) Y: Gambling Rev(\$1000) X*Y X^2 1 42 58 2436 1764 2 48 66 3168 2304 3 62 84 5208 3844 4 76 95 7220 5776 5 82 101 8282 6724 6 99 119 11781 9801 mean 68.2 87.2 sum 409 523 38095 30213 Obj100 Obj101

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5/20/10 Simple Linear Regression - Descriptive Obser v X: ATM Disbur. (\$1000) Y: Gambling Rev(\$1000) (Yi- Ybar)^2 Y-Hat ei ei^2 X*Y X^2 1 42 58 852.64 59.7 1.7 2.89 2436 1764 2 48 66 208849 66 0 0 3168 2304 3 62 84 7056 80.7 -3.3 10.89 5208 3844 4 76 95 9025 95.4 0.4 0.16 7220 5776 5 82 101 10201 101.7 0.7 0.49 8282 6724 6 99 119 14161 119.55 0.55 0.3025 11781 9801 mean 68.2 87.2 sum 409 523 250145 523 0 15 38095 3021 3 SST o SSE R2 = SSR/SSTo The amount of variation that can be explained from our model
5/20/10 Simple Linear Regression - Inferential Y i ~ ind N( 0 + 1Xi, 2) β β σ Assumptions: 1) Independence: random sampling 2) Normality: NPP of residuals 3) Linearity: Scatter plot 4) Constant Variance: Residual versus Fits 5) Outliers: several plots, Cooks Distance

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5/20/10 Simple Linear Regression - Inferential s2 = SSE/n-2 = MSE Point estimate: and Standard Error come right from regression output: Coefficient = Point Estimate SE Coef = Standard Error Regression Analysis: 2008 versus 2007 The regression equation is 2008 = 1.44 + 1.09 2007 Predictor Coef SE Coef T P Constant 1.4360 0.1372 10.47 0.000 2007 1.08870 0.00686 158.69 0.000 S = 1.03497 R-Sq = 99.6% R-Sq(adj) = 99.6% Analysis of Variance Source DF SS MS F P Regression 1 26975 26975 25182.96 0.000 Residual Error 98 105 1 Total 99 27080
5/20/10 Simple Linear Regression: Inferential Regression Analysis: 2008 versus 2007 The regression equation is 2008 = 1.44 + 1.09 2007 Predictor Coef SE Coef T P Constant 1.4360 0.1372 10.47 0.000 2007 1.08870 0.00686 158.69 0.000 S = 1.03497 R-Sq = 99.6% R-Sq(adj) = 99.6% Analysis of Variance Source DF SS MS F P Regression 1 26975 26975 25182.96 0.000 Residual Error 98 105 1 Total 99 27080 Is B1 greater than 1? Hypothesis Test H0 :B1 = 1 HA :B1 > 1 TS: = (1.08870 – 1) / .00686 = 12.930 Find the p value using a T distribution with n-2 degrees of freedom and compare with alpha

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5/20/10 Simple Linear Regression: Inferential ANOVA table for regression The F-Test above is a test to see if the linear relationship of y with x explains a statistically significant amount of the variation in y.
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