Answer to Question #250445 in Macroeconomics for GTee

Question

Two researchers, Mamelodi and Phatane report the results of an investigation into the factors affecting the quantity Yt of wheat produced in Thohoyandou, Limpopo province of South Africa, using annual data from 1995 to 2015. The following regression was run and the estimated equation was found to be: Yt = 993.633 + 0.0461It + 0.706 Dt + 48.22Rt (1368.4) (0.273) (0.945) (11.28) Standard error of estimates are in parenthesis Adjusted R2 = 0.56 Where It, Dt, and Rt were hectares of irrigated area, hectares of dry land area and rainfall respectively.
a) Estimate t-value for each of the predictor variables in the model (b) Briefly explain why Mamelodi and Phatane may have concluded that the result did not make sense. c) In order to improve the model, the two researchers added the variable T (time) and obtained: Yt = -0.740 + 0.578 It + 0.218 Dt + 46.6 Rt à ƒ ¢ € “ 40.4 Tt (1755) (0.442) (0.959) (10.9) (26.9) St

Answer 1

The regression is a method of machine learning under subgroup Supervised Learning. The regression helps to get the relation between the dependent and the independent variables.

The regression equation is obtained by using the given data is used to predict or forecast the values of new data. It can also be used for understanding and analyzing the relation between the variables.

a) For 'It' variable:

The test statistics is 

$t=\frac{b_{lt}}{S.E._{lt}}\\=\frac{0.04}{60.273}\\=0.1684982$

For 'Dt' variable:

The test statistics is 

$t=\frac{b_{Dt}}{S.E._{Dt}}\\=\frac{0.706}{0.945}\\=0.7470899$

For 'Rt' variable:

The test statistics is 

$t=\frac{b_{Rt}}{S.E._{Rt}}\\=\frac{48.22}{11.28}\\=4.274823$

Therefore, the t-value for 'It', 'Dt' and 'Rt' variables are 0.1684982, 0.7470899 and 4.274823.

b) The R - Square for the given model is 0.56.

R - Square also called the coefficient of determination, is the value between 0 and 1 which explains how good is the model that is the variance of the dependent variable that can be explained from the variance of the independent variable.

Now, since the R - Square for the model is around 50% means that the model is not that good.