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					                      Modeling Using Cubic Regression


   Copy the data set below into Excel:
             x             y
           -0.2          4.2
            0.3          3.7
            0.9         -0.98
            2.3          -3.8
            2.9          6.87


Create a scatterplot (y vs x) of the data in Excel and paste your graph
below:




   Find a quadratic regression model ( y  ax 2  bx  c ) for the data and
   report the model below. What is the value of r-squared for this model?

                                



   Find a cubic regression model ( y  ax 3  bx 2  cx  d ) for the data and
   report the model below. What is the value of r-squared for this model?

                          




   Which model is a better fit for the data? How do you know?




  Use the superior model to predict the value of y when x=0.
                      Modeling Using Cubic Regression




Real Estate The table shows the average price (in thousands of dollars) of a
house in the Northeastern U.S. for 1987 to 1995. Let t be the number of
years since 1987.
                               t           f(t)
                               0           140
                               1           149
                               2          159.6
                               3           159
                               4          155.9
                               5           169
                               6          162.9
                               7           169
                               8           180



Create a scatterplot (Average Home Price vs. Year) of the data in Excel and
paste your graph below:




   Find a quadratic regression model ( y  ax 2  bx  c ) for the data and
   report the model below. What is the value of r-squared for this model?

                             
   Find a cubic regression model ( y  ax 3  bx 2  cx  d ) for the data and
   report the model below. What is the value of r-squared for this model?

                          

   Which model is a better fit for the data? How do you know?



   Use the superior model to predict the price of a home in the year 2000.
                      Modeling Using Cubic Regression


Space Exploration The table shows the average speed y (in feet per
second) of a space shuttle for different times t (in seconds) after launch.

                                t           y
                               10         202.4
                               20         463.4
                               30         748.2
                               40         979.3
                               50         1186.3
                               60         1421.3
                               70         1795.4
                               80         2283.5



Create a scatterplot (Average Speed vs Time after Launch) of the data in
Excel and paste your graph below:




   Find a quadratic regression model ( y  ax 2  bx  c ) for the data and
   report the model below. What is the value of r-squared for this model?

                               

   Find a cubic regression model ( y  ax 3  bx 2  cx  d ) for the data and
   report the model below. What is the value of r-squared for this model?

                          

   Which model is a better fit for the data? How do you know?




   Use the superior model to determine the speed of the space shuttle 100
   seconds after the launch.

				
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