3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁ -0.047X2; +0.032X3; -0.018.X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic = 1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁i = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X3₁ = Price of wine and sprits in year t (index number with 2001 = 100) X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw from the value of the Durbin-Watson statistic? Do your conclusions alter your answer to (c) ?

3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁ -0.047X2; +0.032X3; -0.018.X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic = 1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁i = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X3₁ = Price of wine and sprits in year t (index number with 2001 = 100) X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw from the value of the Durbin-Watson statistic? Do your conclusions alter your answer to (c) ?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.4: Linear Regression

Problem 12SBE: Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

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Question

100%

3. A study of beer consumption using the annual data from 1980 -2001 produced the
following regression:
Y = 0.41 +0.052.X₁; −0.047X2; +0.032X3; −0.018X4i
(0.027) (0.011) (0.009) (0.008) (0.009)
R² = 0.94 F = 66.58 DW statistic=1.32, figures in the brackets are standard errors
Where:
Y₁ = Annual aggregate beer consumption in year t (billion pints)
X₁₁ = Real disposable income income in year t ($ billions at 2001 prices)
X2i = Price of beer in year t (index number with 2001 = 100)
X31 Price of wine and sprits in year t (index number with 2001 = 100)
=
X4₁ = Price of cigarettes in year t (index number 2001 = 100)
(a) What is the effect of a change in the price of beer on beer consumption? Does it have
the correct sign? Explain.
(b) Comment on the signs of the other three coefficients. Are they as expected?
(c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4.
What assumptions have you made in carrying out these tests?
(d) What conclusion do you draw from the value of the Durbin-Watson statistic? Do your
conclusions alter your answer to (c) ?

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