Question

Regression model>BEEF_CONSt - Bl B2INCOMEt+B3BEEF PRICEt B4PORK PRICEt+ et BEEF CONSIconsumption of beef per capita in year t (kg), INCOMEt real income per capita in year t (thousands of dollars), BEEF PRICEt average real price of beef per kilogram in year t ($) PORK PRICEt= average real price of pork per kilogram in year t (S) Bk's regression cocfficients, and et is the random error term, which follows N(0, o2) Gretl Output for Section 2 Sunmary Stati stics Mean Median s.D. Min Max BEEF CONS INCOME BEEF RICE 6.006 5.410 3.679 1.600 18,70 77,88 50.08 73.40 46.28 24.32 16.99 35.20 144.6 24.00 85.05 41.99 39.72 18.35 88.67 PORK PRICE 11.40 Model: OLS, using observations 1-30 Dependent variable: BEEF CONS std. erroE coefficient t-ratio p-value -0.332474 0.112156 -0.0668894 const 2.11033 0.0167339 0.0242290 -0.1575 .702 -2.761 0.8760 4.12e-07 0.0104 INCOME SEEF PRICE PORK PRICE 0.0227048 0.0224709% 1.010 0.3216 Mean dependent var Sum squared resid 6.005833 s.D. dependent var s.E. of regression Adjusted Rquared 3.679292 124.4493 2.187810 R-squared 0.682995 0.646418 Analyais of Variance: Sum of squares df Mean square Regression Residual Total 268.129 89.3764 4.78651 13.5372 124.449 24 392.579 Covariance matrix of regression coefficients: BEEF PRICE 0.033105 INCOME РORK PRICЕ -0.0239675 const const 4.45349 -0.0209248 2.80022-04 9.25173-08 5.8704 3e-04 -2.11457e-05 INCOME 8.80824-05 BEEF RICE 5.04943e-04 ORK PRICE Breusch-Pagan test for heteros kedasticity OLS, using observations 1-30 Dependent variable: scaled uhat 2 (Koen ker robust variant std. error coefficient -value t-ratio -4.36350 0.0156113 4.24597 0.0336684 -1.028 0.4637 0.3136 0.6467 conat нсоE BEEF PRICE PORK PRICE 0.00539918 0.0487485 0.1108 0.9127 0.0685217 0.0452114 1.516 0.1417 Explained sum of squares -50.7517 Teat atatiaties -2.745627 . Elasticity and goodness-of-fit (a) What is the elasticity of beef consumption with respect to beef price when evaluated at the sample mean values of the variables? Interpret the elasticity (b) Interpret the coefficient of determination (R2). 2. Heteroscedasticity (a) Test for heteroscedasticity using the Koenker variant of Breusch-Pagan test at 5%. (b) What are the consequences of heteroscedasticity when all the other standard assumptions are satisfied? p3 0 against H1: 2+B3> 0 at 5 %. Your answer must include an 3. Test H0: B2 interpretation of the test result in terms of the relationship between the effect of income and the effect of beef price on beef consumption.

Answer 1

1.

a) The Elasticity of beef consumption with respect to beef price is -0.06685 which means that if beef price increased by one unit (and other dependent variables remained constant), beef consumption will decrease by 0.06685 units on an average.

b) R2 (Coefficient of determination R sq-0.68299 in this example) is the statistical measure of how close the data to the fitted regression line i.e. it explains the variation of response variables explained by the model. That means in this example 68% of the total variation is explained by the model. Higher the R2, better the model.

2.

a) The test for heteroscedasticity is already given in the output.

As p-values of all dependent variables in the data are >0.05, we accept H0 i.e. the assumption of heteroscedasticity is not valid.

b) If the variance of the errors is increasing , confidence intervals for sample predictions will tend to be narrow. Heteroscedasticity may also have the effect of giving too much weight to a small subset of the data when estimating coefficients.