How well does the linear mathematical model fit the data? This activity explores the goodness of fit of a linear regression model to data using an interactive Excel spreadsheet. The questions are grouped into categories that use one of the four different worksheets as labeled by the tabs at the bottom of the computer screen. For any of the worksheets, adjusting the scroll bar parameters will generate a new set of data, which will re-plot and the regression will respond accordingly, Scatter in data - Scatter tab A common measure of the goodness of fit is the re value. Vary the scatter by moving the scroll bar or clicking on the arrows on the worksheet. How does r? vary with the scatter of the data about the regression line? 20 What is the value of r? for a perfect fit? 1 The use of r' as a measure of the goodness of fit is realistic because it describes the fraction (or if multiplied by 100, the percentage) of the y-variable that is explained by the variation of the x-variable. A perfect fit of a regression equation to the data generates an rvalue of one. For 10 data points, an r?> 0.795 is needed at the 95% confidence level to have statistical significance. Can you generate data with enough noise or scatter so it is not a significant relationship