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 below:

(A) Given the nature of the problem, which would be the dependent variable and which would be the independent variables?

(B) 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.

(C) 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.

(D) 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.

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

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

(G) Interpret the coefficients of the independent variables based on the best model.

(H) Also, describe the demand for ice cream with respect to P_ic, I, T and indicate the relationship between ice cream and cappuccino.

(I)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.

(J)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?

Year P. (S/kg) I (S) T P. (S/kg) 2000 72000 11 2000 20 14 2001 81000 10 2100 24 15 2002 90000 9 2200 25 15 2003 99000 7 2305 26 16 2004 108000 6 2407 30 17 2005 126000 4 2500 32 18 2006 117000 7 2610 26 16 2007 117000 8 2698 25 16 2008 135000 5 2801 31 18 2009 135000 2921 3 18 2010 144000 4 3000 34 20 2011 180000 2 3099 36 21 2012 162000 5 3201 33 19 2013 171000 4 3308 35 21 2014 153000 6 3397 30 18 2015 180000 3 3501 35 22 2016 171000 4 3689 33 20 2017 180000 3 3800 36 23 2018 198000 2 3896 36 25 2019 189000 4 3989 34 23 2020 175000 6 3600 30 18