Input the following data into Excel. 9) Assume that Q = quantity of pizza, X1 = price of pizza (in cents), X2 = tuition (in thousands of dollars), X3...

Input the following data into Excel.

9)          Assume that Q = quantity of pizza, X1 = price of pizza (in cents), X2 = tuition (in thousands of dollars),

             X3 = price of soft drinks (in cents):

Q           X1                        X2                        X3

Pizza     Price of Pizza      Tuition                Price of Soda

12         110                      13                        100       

10         110                      10                        125       

10         125                      14                        130       

12         110                      15                         80        

11         150                      16                         90        

12         100                      12                         95        

10         150                      12                      100       

 8          160                      10                         90        

 9          150                      13                         95        

10         135                      15                        100       

11         125                      16                         95        

12         100                      17                        100       

13          75                      10                        100       

10         100                      12                        110       

 9          110                       6                        125       

 8          125                      10                         90        

 8          150                      5                          80        

 4          100                      0                           95        

a)          Estimate the linear demand function with Q as the dependent variable and X1 as the independent variable. Is this a good model? How do you know (explain relevant results)? The form of the model is . 

b)          Estimate the linear demand function with Q as the dependent variable and X1, X2, X3, as the

             independent variables.  Is this a better model than in a)? How do you know

             (explain relevant results)?

c)          Take the natural logs of Q, X1, X2, and X3 and estimate this version of the D function. Is this a better

             model than that of a) or b)? Why (explain relevant results)?.

d)          What is the value of the price elasticity of demand? What is the value of the cross-price elasticity of demand? 

Input the following data into Excel.

10)        Assume we have the following time series data on variable Y below:

YEAR                   Y

1991                    8649

1992                    8660

1993                    8680

1994                    8726

1995                    8740

1996                    8760

1997                    8783

1998                    8805

1999                    8812

2000                    8854

2001                    8841

2002                    8869

2003                    8893

2004                    8883

2005                    8888

2006                    8904

2007                    8913

2008                    8913

2009                    8923

2010                    8948

2011                    8962

a)          Fit a simple trend model to the time series data and discuss the findings. 

             This model can be written as

b)          Fit a quadratic trend model to the time series and discuss the findings. 

             Hint: [If the model in a) is written as, how is the model in b) different?]

c)          Compare your results in part b) to part a)

d)          use the best of the two models to forecast the 2012 value of Y.