The following table gives the quantity demanded of ice cream (Qic) in kgs per year in Sardinia (Italy), its price (Pic) in $ per kg, consumers’ income (I) in $, the temperature (T) in Celsius, and the price of cappuccino (Pc) in $ per kg: Year Qic Pic ($/kg) I ($) T Pc ($/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 5 2921 31 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 Based on the data provided in the table: 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. y = 12114.23 -39388.14 Pic + 42.94 I +1135.405 T - 646.66 Pc 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. Qs = 3.14964 - 0.2027 In Pic +1.163 In I + 0.5844 InT - 0.7818 InPc 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 Pic, 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 Pic = $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?

The following table gives the quantity demanded of ice cream (Qic) in kgs per year in Sardinia (Italy), its price (Pic) in $ per kg, consumers’ income (I) in $, the temperature (T) in Celsius, and the price of cappuccino (Pc) in $ per kg: Year Qic Pic ($/kg) I ($) T Pc ($/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 5 2921 31 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 Based on the data provided in the table: 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. y = 12114.23 -39388.14 Pic + 42.94 I +1135.405 T - 646.66 Pc 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. Qs = 3.14964 - 0.2027 In Pic +1.163 In I + 0.5844 InT - 0.7818 InPc 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 Pic, 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 Pic = $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?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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The following table gives the quantity demanded of ice cream (Qic) in kgs per year in Sardinia (Italy), its price (Pic) in $ per kg, consumers’ income (I) in $, the temperature (T) in Celsius, and the price of cappuccino (Pc) in $ per kg:

Year	Qic	Pic *($/kg)*	I *($)*	T	Pc *($/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	5	2921	31	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

Based on the data provided in the table:

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.

y = 12114.23 -39388.14 Pic + 42.94 I +1135.405 T - 646.66 Pc

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.

Qs = 3.14964 - 0.2027 In Pic +1.163 In I + 0.5844 InT - 0.7818 InPc

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 Pic, 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 Pic = $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?

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