Answer to Question #272325 in Macroeconomics for Maphula

Question

a) A researcher estimated the following regression equation for sorghum production, 

Yt from the use of various amounts of fertilizer, X1 and insecticides X2 on a hectare 

basis using time series data from 2001 to 2010.

The operation model is:

Yt = B0 + B1X1 + B2X2 + ei

The estimated regression equation is:

Yt = 31.98 + 0.65X1 + 1.10X2

(0.24) (0.27) (0.25)

Adjusted R2 = 0.989

Figures in parenthesis are standard error of estimates.

i) Estimate the t-values for each of the coefficients

ii) Interpret the results 

Answer 1

i)we will show the model in Excel:

t-statistics - calculated values of the t-criterion calculated by the formula:

$t-statistics =\frac{Coefficients}{ Standard error}$

ii) If R-squared > 0.95, they say that the approximation accuracy is high (the model describes the phenomenon well). If the R-square lies in the range from 0.8 to 0.95, they speak of a satisfactory approximation (the model as a whole is adequate to the described phenomenon). If R-squared < 0.6, it is assumed that the accuracy of the approximation is insufficient and the model requires improvement (introduction of new independent variables, consideration of nonlinearities, etc.).

The normalized R-square is the adjusted (adapted, corrected) coefficient of determination.

The value of t-statistics (Student's criterion) helps to assess the significance of the coefficient with an unknown or free term of linear dependence. If the value of the t-criterion is > tcr, then the hypothesis of the insignificance of the free term of the linear equation is rejected.