Simple Linear Regression Equation (Line of Best Fit / Prediction line) ? ̂ = β ̂ 0 + β ̂ 1 ? where ? ̂ = dependent variable (the predicted value) ? = independent variable (your known value) β ̂ 0 = y-intercept β ̂ 1 = slope Independent variable X Dependent variable Y Amount of shelf space Monthly Sales Line of Best Fit
13 Example 3 The 759 store’s goal is to forecast annual sales for all new stores, based on store si ze. To examine the relationship between the store size in square feet and its annual sales, a sample of 14 stores was selected. The following table summarizes the results for these 14 stores, which are stored in the file site .xls Step 1) Construct a scatter plot. Observe the increasing relationship between square feet (X) and annual sales (Y). As the size of the store increases, annual sales increase approximately as a straight line. Thus, you can assume that a straight line provides a useful mathematical model of this relationship. Now you need to determine the specific straight line that is the best fit to these data.
14 Step 2) Find the line of best fit Click Analyze > Regression > Linear... Descriptive Statistics Mean Std. Deviation N Annual Sales 5.843 2.9994 14 Square Feet 2.921 1.7080 14 Correlations Annual Sales Square Feet Pearson Correlation Annual Sales 1.000 .951 Square Feet .951 1.000 Sig. (1-tailed) Annual Sales . .000 Square Feet .000 . N Annual Sales 14 14 Square Feet 14 14