Question

7 Consider the following regression output involving the variables y and, rı, r2. (note log is the natural logarithm as usual) 4.12 0.88 r Model A: Model B: log(y)0.34 0.14 + 0.001 2 Model C: logly)2011.4 log()0.02 r2 0.06 Model D: Model E: y = 5.4 + 0.82i --3.4 55.1 log(0.020 2 + 1.2r2 0.2 (1x2) Ceteris Paribus: (a) In Model A: If x1 increases 6 to 8 by 2 units, then the predicted change in y is Δy = (b) In Model B: Ifx1 increases by 2 units, the estimated change in y is (c) In Model C: the elasticity of y with respect to x1 is estimated If the change in x1 is 100%, the estimated change in y is (d) In Model D: 11x1 changes by 100%, the estimated change in y is (e) In Model D: In order for the increase in yr to be 2 units we must have Δx,- (f) In Model E: Given ΔΧ1-1 and X2-2, what is the predicted change in y: Δy®-......... 2. State whether the following statements are (T)RUE or (F)ALSE. (a) (...., When a new variable is added to a regression model R2 always increases (or remains the same) (b) (....) The sum of residuals is always zero. (c) (.....) In the regression analysis, we do not allow any correlation among explanatory variables. (d) (.) We can use perfectly collinear variables in the regression analysis. (e) (.....) When we change units of measurements of X variables, OLS estimators remain the same (f) (.....) As the degrees of freedom increases, t-static approaches the standard normal distribution.

Answer 1

a)Definition of slope coefficient : The coefficient of x is equal to the change in y when there is an unit change in x.
Hence, for 2 units change in x1, the predicted change in y = 2 * coefficient of x1 = 2*0.88 = 1.76

b) For 2 units change in x1, the estimated change in log y = 2 * coefficient of x1 = 2*0.14 = 0.28
hence, estimated change in y = e^0.28 = 1.323

c) As per definition of elasticity, E = dy/dx . (x/y) , for the equation log(y) = a + b1.log(x1) + b2x2,
we get E = b1.
Thus, elasticity of y with respect to x1 is estimated as -1.4.
Since x1 is logged, b1 is the estimated change in log(y) for 100% change in x1.
Thus, estimated change in y = e^-1.4 = 0.2466.

d) Since x1 is logged, the estimated change in y for 100% change in x1 = 55.1.