1) Input the following data into Excel. Or, you may open the Regression Homework Q1 data Excel file Assume that Q = quantity of pizza, Price = price of pizza (in cents), Tuition = tuition (in...

1)
Input the following data into Excel.
Or, you may open the Regression Homework Q1 data Excel file
Assume that Q = quantity of pizza, Price = price of pizza (in cents), Tuition = tuition (in thousands of dollars), Price of Soft Drink = price of soft drinks (in cents):
Q    Price        Tuition        Price of Soft Drink
10    100        14        120    
12    100        16         95    
13     90         8        110    
14     95         7         90    
9    110        11        100    
8    125         5        100    
4    125        12        125    
3    150        10        150    
15     80        18        100    
12     80        12         90    
13     90         6         80    
15    100         5         75    
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        10         95    

a) Estimate the linear demand function with Q as the dependent variable and Price as the independent
variable. Comment fully on the results and discuss the identification problem.
)    Estimate the linear demand function with Q as the dependent variable and Price, Tuition, Price of Soft
    Drinks, as the independent variables. Comment fully on the results.
c)    Take the natural logarithm of all the variables and estimate the new demand function. Comment fully on
    the results. What is the value of the price elasticity of demand? What is the value of the cross-price
    elasticity of demand?
2)
Input the following data into Excel.
Regression Homework Q2 data Excel file
Assume we have the following time series data on variable Y below:
YEAR/Time    Y=Output
1953        482
1954        312
1955        1221
1956        1800
1957        2419
1958        2958
1959        3454
1960        3897
1961        4317
1962        4705
1963        5056
1964        5378
1965        5681
1966        5964
1967        6216
1968        6425
1969        6632
1970        6836
1971        7003
1972        7170
1973        7315
1974        7456
1975        7595
1976        7715
1977        7815
1978        7918
1979        7995
1980        8079
1981        8164
1982        8239
1983        8292
1984        8355
1985        8402
1986        8461
1987        8493
1988        8539
1989        8561
1990        8609
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.
)    Fit a quadratic trend model to the time series and discuss the findings: (square time).
c)    Compare your results in part (b) to part (a) and use the best of the two models to forecast 2012 and 2013
    values of Y.