MBA统计学第10课.ppt

Relationship among variables Functional relationship Statistical relationship(correlation) Y depends on X, but isn’t merely determined by X. Example: price and sales daily high temperature—the demand for air-conditioning Regression—According to observed data, establish regression equation and make statistical reference (predict) . Example: X-price，Y-sales for a kind of product We collect data: 1. Scatter plot 2. Regression equation(the Least Square Estimation) 3. Correlation coefficient (Testing the regression model) 4.Forecasting (point and interval forecasting ) Significance Test Test Coefficient of Determination and Standard Deviation of Estimation Residual Analysis A measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variation in the dependent variable y that is explained by the estimated regression equation. 1. Tests a Linear Relationship Between X Y 2. Hypotheses H0: ?1 = 0 (No Linear Relationship) H1: ?1 ? 0 (Linear Relationship) 3. Test Statistic H0: ?1 = 0 H1: ?1 ? 0 ? ? .05 df ? 5 - 2 = 3 Critical value: There exists linear relationship among an dependent variable and two or more than two independent variables. You work in the advertisement department of New York Times(NYT). You will find to what extent do ads size(square inch ) and publishing volume (thousand) influence the response to ads(hundred). 1.Slope (b1) If the publishing volume remains unchanged,when ads size increases one square inch, the response is expected to increase 0.2049 hundred times. 2.Slope (b2) If ads size remains unchanged, when publishing volume increases one thousand, the response is expected to in- crease 0.2805 hundred times. 1. How does the model describe the relationship among variables? 2. Closeness of ‘Best Fit’ 3. Assumptions met 4. Significance of estimates 5. Correlation among variables 6. Outliers (unusual observations) Non-linear models that can be transf