1 Introduction to Regression Analysis We wish to study the relationship between 2 or more variables We define: y = the dependent variable x = independent (predictor) variable We wish to predict y on the basis of x . Example: y = sales of a product x = price of the product Assuming a linear (straight line) relationship between y and x, we wish to find a prediction equation Predicted value of y intercept y ˆ = b0 + b 1 x slope Simple Linear Regression One Straight Line Predictor Relationship Variable We use data concerning both x and y to find numerical values for b0 and b 1 .
Multiple Regression We predict y by using more than one independent (predictor) variable. Example: y = sales x 1 = price x 2 = advertising budget x 3 = type of advertising ( TV, radio, print, etc.) The prediction equation might have the following form: y ˆ = b0 + b 1 x 1 + b 2 x 2 + b 3 x 3 We find numerical values of b0 , b 1 , b 2 , and b 3 by using data concerning y , x 1 , x 2 , and x 3 . Alternatively, ( as one possible example) the prediction equation could have the form:
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