2_Regr_Linear_Quad-Robert Esposito

Comparison of Linear and Quadratic Regression Models Name:________________________________________ Section:___________ The following data presents the growth in worldwide Internet usage from 1995 through 2011: Year: 1995 1996 1997 1998 1999 2000 2001 No. of users (in millions): 16 36 70 147 248 361 533 Year: 2002 2003 2004 2005 2006 2007 2008 No. of users (in millions): 597 719 817 1018 1093 1319 1574 Year: 2009 2010 2011 No. of users (in millions): 1802 2013 2267 1. Enter the data into L1 and L2 and create a linear model for the data: a. What is your linear model? a. Y=139.8x – 279186.3 b. What is the slope? a. 139.8 c. Interpret the slope within the context of the problem. a. Approx. as one year goes by, there is an increase of 139,800,000 internet users d. What is the r-value? _______ What does this tell you about the linear relationship between x and y? a. 0.9778 b. There is a positive association between the data, as y increases, x increases

e. What is the r 2 value? What does this tell you about the relationship between x and y? a. 0.9561 b. Since the number is very close to 1, it is a great representation of the data f. Do a scatterplot of Y1 and the data. What does that tell you about the linear model? a. Confirms the positive slope in the model g. Store the predictions in L3 and the Residuals in L4. a. The model is not a good method of representing the data h. Do a scatterplot of X-values vs Residuals. When doing this plot, first Deselect Y1. Sketch the plot here. What does this tell you about the linear model? a. i. Create a quadratic model: a. Y = 6.65x^2 – 26518.3x + 26418731.4 j. What is the R 2 value? What does this tell you about the relationship between x and y? a. 0.9973 k. Do a scatterplot of Y1 and the data. What does that tell you about the quadratic model? a. The quadratic regression is the better representation of the data l. Store the predictions in L3 and the Residuals in L4.