Jenkins 11 stats

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University Of Connecticut *

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Statistics

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Apr 3, 2024

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Comparison of Linear and Quadra1c Regression Models Name:________________________________________ Sec1on:___________ 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?___________________________ b. What is the slope? _____ c. Interpret the slope within the context of the problem. d. What is the r-value? _______ What does this tell you about the linear rela1onship between x and y? e. What is the r 2 value? What does this tell you about the rela1onship between x and y? f. Do a scaWerplot of Y1 and the data. What does that tell you about the linear model? 4 279186 3 139.84 139.8 each unit increase in year theaverage Of Internet users increases 139.8 million 0.97 95 6th of the totalvariation in the Of internet users can be explained by the regression equation 95.6 of total variation in of users can be explained by regression equation
g. Store the predic1ons in L3 and the Residuals in L4. h. Do a scaWerplot of X-values vs Residuals. When doing this plot, Zrst Deselect Y1. Sketch the plot here. What does this tell you about the linear model? i. Create a quadra1c model:___________________________ j. What is the R 2 value? What does this tell you about the rela1onship between x and y? k. Do a scaWerplot of Y1 and the data. What does that tell you about the quadra1c model? l. Store the predic1ons in L3 and the Residuals in L4. m. Do a scaWerplot of X-values vs Residuals. When doing this plot, Zrst Deselect Y1. Sketch the plot here. What does this tell you about the quadra1c model? n. Look at the Residual plot and use the Trace Key to Znd the ‘largest’ residual (it could be posi1ve or nega1ve.) Go back to your Stat Editor and Znd the corresponding x- value, y-value and predicted y-value. o. Use your model stored in Y1 to es1mate the number of internet users for 2012. 4 6.65 2 26518.27 26418731.42 99.71 Quadratic model fit better than linear model scatterplots have no pattern which means the negner reg ea is a better fit 2 498,000,000
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