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4. (2) Using data from 1950 to 1996 (N=47 observations) the following equation for explaining wheat yield in the Mullewa Shire of Western Australia was estimated as YIELD,= = 0.1717+0.01117t+0.05238Rain, (se) (0.1537) (0.00262) (0.01367) Where YIELD, is wheat yield in tonnes per hectare in year t; t =1, 2, ..., 47 is a trend variable to capture technological change, and RAIN, is total rainfall in inches from May to October (the growing season) in year t. a) Interpret the coefficient estimates of t and Rain. b) Using a 5% significance level, test the null hypothesis that technological changes increase mean yield by 0.01 tonnes per hectare against the one-tailed alternative H₁: B₂ >0.01. c) Using a 5% significance level, test the null hypothesis that an extra inch of rainfall increases mean yield by 0.03 tonnes per hectare against the one-tailed alternative H₁: B3 > 0.03. d) Adding the square of rainfall to the equation yields YIELD, = -0.6759+0.011671t+0.2229 Rain, -0.008155 Rain? (se) (0.3875) (0.0025) (0.0734) (0.003453) What is the rationale for including the square of rainfall? Does it have the expected sign? Repeat part (b) using the model in part (d). e) f) Use each model to forecast yield in 1997 (t=48), when rainfall was 9.48 inches. g) Use each model to forecast yield in 1998 (t=49), when rainfall was 18.95 inches.

4. (2) Using data from 1950 to 1996 (N=47 observations) the following equation for explaining wheat yield in the Mullewa Shire of Western Australia was estimated as YIELD,= = 0.1717+0.01117t+0.05238Rain, (se) (0.1537) (0.00262) (0.01367) Where YIELD, is wheat yield in tonnes per hectare in year t; t =1, 2, ..., 47 is a trend variable to capture technological change, and RAIN, is total rainfall in inches from May to October (the growing season) in year t. a) Interpret the coefficient estimates of t and Rain. b) Using a 5% significance level, test the null hypothesis that technological changes increase mean yield by 0.01 tonnes per hectare against the one-tailed alternative H₁: B₂ >0.01. c) Using a 5% significance level, test the null hypothesis that an extra inch of rainfall increases mean yield by 0.03 tonnes per hectare against the one-tailed alternative H₁: B3 > 0.03. d) Adding the square of rainfall to the equation yields YIELD, = -0.6759+0.011671t+0.2229 Rain, -0.008155 Rain? (se) (0.3875) (0.0025) (0.0734) (0.003453) What is the rationale for including the square of rainfall? Does it have the expected sign? Repeat part (b) using the model in part (d). e) f) Use each model to forecast yield in 1997 (t=48), when rainfall was 9.48 inches. g) Use each model to forecast yield in 1998 (t=49), when rainfall was 18.95 inches.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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4. (2) Using data from 1950 to 1996 (N = 47 observations) the following equation for explaining wheat yield in the Mullewa Shire of Western Australia was estimated as YIELD, = 0.1717+0.01117t+0.05238Rain, (se) (0.1537) (0.00262) (0.01367) ... Where YIELD, is wheat yield in tonnes per hectare in year t; t =1, 2, . 47 is a trend variable to capture technolo change, and RAIN, is total rainfall in inches from May to October (the growing season) in year t. a) Interpret the coefficient estimates of t and Rain. b) Using a 5% significance level, test the null hypothesis that technological changes increase mean yield by 0.01 tonnes per hectare against the one-tailed alternative H₁ : ₂ >0.01. c) Using a 5% significance level, test the null hypothesis that an extra inch of rainfall increases mean yield by 0.03 tonnes per hectare against the one-tailed alternative H₁ : B3 > 0.03. d) Adding the square of rainfall to the equation yields YIELD, = -0.6759+0.011671t+0.2229 Rain, -0.008155 Rain? (se) (0.3875) (0.0025) (0.0734) (0.003453) What is the rationale for including the square of rainfall? Does it have the expected sign? Repeat part (b) using the model in part (d). e) f) Use each model to forecast yield in 1997 (t = 48), when rainfall was 9.48 inches. g) Use each model to forecast yield in 1998 (t = 49), when rainfall was 18.95 inches.
Transcribed Image Text:4. (2) Using data from 1950 to 1996 (N = 47 observations) the following equation for explaining wheat yield in the Mullewa Shire of Western Australia was estimated as YIELD, = 0.1717+0.01117t+0.05238Rain, (se) (0.1537) (0.00262) (0.01367) ... Where YIELD, is wheat yield in tonnes per hectare in year t; t =1, 2, . 47 is a trend variable to capture technolo change, and RAIN, is total rainfall in inches from May to October (the growing season) in year t. a) Interpret the coefficient estimates of t and Rain. b) Using a 5% significance level, test the null hypothesis that technological changes increase mean yield by 0.01 tonnes per hectare against the one-tailed alternative H₁ : ₂ >0.01. c) Using a 5% significance level, test the null hypothesis that an extra inch of rainfall increases mean yield by 0.03 tonnes per hectare against the one-tailed alternative H₁ : B3 > 0.03. d) Adding the square of rainfall to the equation yields YIELD, = -0.6759+0.011671t+0.2229 Rain, -0.008155 Rain? (se) (0.3875) (0.0025) (0.0734) (0.003453) What is the rationale for including the square of rainfall? Does it have the expected sign? Repeat part (b) using the model in part (d). e) f) Use each model to forecast yield in 1997 (t = 48), when rainfall was 9.48 inches. g) Use each model to forecast yield in 1998 (t = 49), when rainfall was 18.95 inches.
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