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.
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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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VIEWStep 2: Interpret the coefficient estimate of the t and Rain_t
VIEWStep 3: Perform the test for the β_2>0.01
VIEWStep 4: Perform the test for the β_3>0.03
VIEWStep 5: Determine the rationale for including the rainfall.
VIEWStep 6: Repeat the part b using model in part d.
VIEWStep 7: Calculate the estimated yield for each model.
VIEWStep 8: Calculate the estimated yield for each model.
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