The following table gives the quantity demanded of ice cream ( Q ic ) in kgs per year in Sardinia (Italy), its price ( P ic ) in $ per kg, consumers’ income ( I ) in $, the temperature (T) in Celsius,...

The following table gives the quantity demanded of ice cream (
Q


ic
) in kgs per year in
Sardinia
(Italy), its price (
P


ic
) in $ per kg, consumers’ income (
I
) in $, the temperature (T) in Celsius, and the price of cappuccino (
P


c
) in $ per kg:

Based on the data provided in the table:

• 
  Given the nature of the problem, which would be the dependent variable and which would be the independent variables?
  

• 
  Using the regression facility in Excel, determine the estimated regression line using a
  linear multiple regression. Does this model fit the data? If it does, please write the estimated equation. If not, what do you think the problem might be? How do you know? Please, attach the page of the regression analysis output.
  

• 
  Using the regression facility in Excel, determine the estimated regression line using a
  nonlinear multiple regression. Does this model fit the data? Why? If it does, please write the estimated equation. Please, attach the page of the regression analysis output.
  

• 
  Based on the best model, test the hypothesis that there is no relationship between the demand for ice cream and each one of the independent variables. Also, indicate the statistical significance of each of the independent variables.
  

• 
  Based on the best model, how much is the coefficient of determination? What does it mean?
  

• 
  For the best model, what does the F-test result tell us?
  

• 
  Interpret the coefficients of the independent variables based on the best model.
  

• 
  Also, describe the demand for ice cream with respect to
  P
  ic
  , I, T
  and indicate the relationship between ice cream and cappuccino.
  

• 
  Determine the
  point estimate
  of the demand for ice cream, based on the best regression model, given that the
  P
  ic
  
  = $10/kg , I = $4,000, T = 30 Celsius, and Pc = $20/kg.
  

• 
  Then, construct an approximate 95 percent confidence level
  prediction interval
  of the demand for ice cream.
  

• 
  If you know that the
  Durbin-Watson
  statistic for the data of the this case study is
  1.609, what can you conclude about the possibility of
  autocorrelation?