. Suppose Y is related to R and S in the following nonlinear way:
Y= aRáµSá¶
a. How can this nonlinear equation be transformed into a linear form that can ve analyzed using multiple regression analysis.
Sixty-three observations are used to obtain the following regression results:
DEPENDENT VARIABLE: LNY
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATION: 63
0.8151
132.22
0.0001
VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T-RATIO
P-VALUE
INTERCEPT
-1.386
0.83
-1.67
0.1002
LNR
0.452
0.175
2.58
0.0123
LNS
0.30
0.098
3.06
0.0033
b. Test each estimated coefficient for statistical significance at the 5 percent level of significance. What are the exact significance levels for each of the estimated coefficients?
c. Test the overall equation for statistical significance at the 5 percent level of significance. Interpret the p-value of the F-statistic.
d. How well does this nonlinear model fit the data?
e. Using the estimated value of the intercept, compute an estimate of a.
f. If R = 200 and S = 1,500, compute the expected value of Y.
g. What is the estimated elasticity of R? Of S?
. Suppose Y is related to R and S in the following nonlinear way:
Y= aRáµSá¶
a. How can this nonlinear equation be transformed into a linear form that can ve analyzed using multiple regression analysis.
Sixty-three observations are used to obtain the following regression results:
| DEPENDENT VARIABLE: LNY | R-SQUARE | F-RATIO | P-VALUE ON F | |
| OBSERVATION: 63 | 0.8151 | 132.22 | 0.0001 | |
| VARIABLE | PARAMETER ESTIMATE | STANDARD ERROR | T-RATIO | P-VALUE |
| INTERCEPT | -1.386 | 0.83 | -1.67 | 0.1002 |
| LNR | 0.452 | 0.175 | 2.58 | 0.0123 |
| LNS | 0.30 | 0.098 | 3.06 | 0.0033 |
b. Test each estimated coefficient for statistical significance at the 5 percent level of significance. What are the exact significance levels for each of the estimated coefficients?
c. Test the overall equation for statistical significance at the 5 percent level of significance. Interpret the p-value of the F-statistic.
d. How well does this nonlinear model fit the data?
e. Using the estimated value of the intercept, compute an estimate of a.
f. If R = 200 and S = 1,500, compute the expected value of Y.
g. What is the estimated elasticity of R? Of S?
