Regression analysis for site selection.
Description Lab 3: Simple Regression Analysis Given a desire of a Retail Chain management team to develop a strategy to forecasting annual sales, the following data from a random sample of existing stores has been gathered: STORE SQUARE FOOTAGE ANNUAL SALES ($) 1 1726.00 3681.00 2 1642.00 3895.00 3 2816.00 6653.00 4 5555.00 9543.00 5 1292.00 3418.00 6 2208.00 5563.00 7 1313.00 3660.00 8 1102.00 2694.00 9 3151.00 5468.00 10 1516.00 2898.00 11 5161.00 10674.00 12 4567.00 7585.00 13 5841.00 11760.00 14 3008.00 4085.00 Enter the variable names as follows: Next, by clicking on ‘Data View’, we can enter the data: Assuming, for now, that if a relationship exists between the two variables, it is linear in nature, we can generate a simple Scatterplot (or Scatter Diagram) for the data. This is accomplished with the command sequence: Which yields the following (editable) scatterplot: We can generate a simple straight-line equation from the output resulting when using the Enter Command in regression: Regression Variables Entered/Removeda Model Variables Entered Variables Removed Method 1 Square Footageb . Enter a. Dependent Variable: Annual Sales in Dollars b. All requested variables entered. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .954a .910 .902 $936.850 a. Predictors: (Constant), Square Footage ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 106208119.686 1 106208119.686 121.009 .000b Residual 10532255.243 12 877687.937 Total 116740374.929 13 a. Dependent Variable: Annual Sales in Dollars b. Predictors: (Constant), Square Footage This is the intercept Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 901.247 513.023 1.757 .104 Square Footage 1.686 .153 .954 11.000 .000 This is the slope a. Dependent Variable: Annual Sales in Dollars How to write up regression: A linear regression was used to test the hypothesis that time in minutes would predict understanding. The overall model was significant in that R = .97, F(1, 222) = 579.32, p < .001. As time in minutes increased, understanding also increased. Regression Equation(y) = a + bx where x and y are the variables. b = The slope of the regression line a = The intercept point of the regression line and the y axis. X = First Score Y = Second Score you are predicting for Square footage: Please solve for the following square footage: x = 1. 300 2. 5000 3. 6000 4. 4498 5. 6600 6. 2200 7. 3450 8. 1700 9. 1000 10. 9000 Example: for number 1. Y = 901.247 + 1.686(300) 901.247 + 505.8 = $1407.047