Comparison of Linear and Quadratic Regression Models
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Comparison of Linear and Quadratic Regression Models
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 relationship between x and y?
e. What is the r2 value? What does this tell you about the relationship between x and y?
f. Do a scatterplot of Y1 and the data. What does that tell you about the linear
model?
g. Store the predictions in L3 and the Residuals in L4.
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?
i. Create a quadratic model:___________________________
j. What is the R2 value? What does this tell you about the relationship between x and y?
k. Do a scatterplot of Y1 and the data. What does that tell you about the quadratic model?
l. Store the predictions in L3 and the Residuals in L4.
m. 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 quadratic model?
n. Look at the Residual plot and use the Trace Key to find the ‘largest’ residual (it could be positive or negative.) Go back to your Stat Editor and find the corresponding x- value, y-value and predicted y-value.
o. Use your model stored in Y1 to estimate the number of internet users for 2012.
2023-02-18