Y = a R b S c T d The computer output from the regressions analysis is: DEPENDEN
ID: 1187466 • Letter: Y
Question
Y = a RbScTd
The computer output from the regressions analysis is:
DEPENDENT VARIABLE:
LNY
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS:
32
0.7766
32.44
0.0001
PARAMETER
STANDARD
VARIABLE
ESTIMATE
ERROR
T-RATIO
P-VALUE
INTERCEPT
-0.6931
0.32
-2.17
0.0390
LNR
4.66
1.36
3.43
0.0019
LNS
-0.44
0.24
-1.83
0.0774
LNT
8.28
4.6
1.80
0.0830
a. Are the parameter estimates statistically significant at the 90% level of confidence?
b. If R=1, S=2, and T=3, what will be the value of Y?
c. If R decreases by 10% (all other things constant), what will happen to Y?
DEPENDENT VARIABLE:
LNY
R-SQUARE
F-RATIO
P-VALUE ON F
OBSERVATIONS:
32
0.7766
32.44
0.0001
PARAMETER
STANDARD
VARIABLE
ESTIMATE
ERROR
T-RATIO
P-VALUE
INTERCEPT
-0.6931
0.32
-2.17
0.0390
LNR
4.66
1.36
3.43
0.0019
LNS
-0.44
0.24
-1.83
0.0774
LNT
8.28
4.6
1.80
0.0830
Explanation / Answer
Y = a RbScTd
ln Y = ln a + bo*ln R + b1*ln S + b2*ln T
a) Parameter estimates are statistically sifnificant at 90% confidence interval as the P-value < 0.1 and the calculated t ratios are greater than the tabulated values.
b) ln a is the intercept
ln Y = -0.6931 + 4.66*ln1 - 0.44*ln2 + 8.28*ln3
ln Y = 8.098
Y = 3289.28
c) Y = a RbScTd
ln Yo = -0.6931 + 4.66*lnRo - 0.44*lnSo + 8.28*lnTo
ln Y1 = -0.6931 + 4.66*ln0.9*Ro - 0.44*lnSo + 8.28*lnTo
lnY1 - lnYo = 4.66(ln0.9Ro-lnRo)
ln(Y1/Yo) = 4.66(ln(0.9Ro/Ro)
ln(Y1/Yo) = 4.66(ln(0.9)
ln(Y1/Yo) = 4.66*-.105
Y1/Yo = e^-.491
Y1 = .612Yo
% decrease in Y = (.612Yo-Yo)/Yo * 100% = 38.8%
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