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# Multiple Regression Analysis

In Microsoft Excel, please respond to all questions and math problems in the following problem. See Attachment. Please show Microsoft Excel formula(s) work.

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Problem 1: Twenty-six observations

1. Suppose Y is related to R and S in the following nonlinear way: Y = aRbSc
a. In order to estimate the parameters a, b, and c, the equation must be transformed into the form: ___________________________________.

Twenty-six observations are used to obtain the following regression results:
DEPENDENT VARIABLE: LNY R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 26 0.3647 4.21 0.0170
VARIABLE PARAMETER STANDARD T-RATIO P-VALUE
ESTIMATE ERROR

INTERCEPT 2.9957 0.3545 8.45 0.0001
LNR 2.34 0.87 2.69 0.0134
LNS -0.687 0.334 -2.06 0.0517

b. There are __________ degrees of freedom for the t-test. At the 1% level of significance, the critical t-value for the test is ________________.
c. At the 1% level of significance, a? ____________ (is, is not) significant, b? __________ (is, is not) significant, and ? c ___________ (is, is not) significant.
d. The estimated value of a is __________________.
e. The p-value for b? indicates that the exact level of significance is _______ percent, which is the probability of _________________________________.
f. At the 1% level of significance, the critical value of the F-statistic is _________. The model as a whole ___________ (is, is not) significant at the 1% level.
g. If R = 12 and S = 30, the fitted (or predicted) value of Y is _____________.
h. The percentage of the total variation in the dependent variable not explained by the regression is _______________ percent.
i. If R increases by 14%, Y will increase by ________ percent.
j. A 6.87% increase in Y will occur if S ________________ (increases, decreases) by _______ percent.

#### Solution Preview

Problem 1: Twenty-six observations
1. Suppose Y is related to R and S in the following nonlinear way: Y = aRbSc
a. In order to estimate the parameters a, b, and c, the equation must be transformed into the form: _ln(Y) = ln(a) + b*ln(R) +c*ln(S)___.
I assume that the question is supposed to read Y = a * Rb * Sc (b and c are exponents). Is that correct? If so, then you need to take the logarithm of both sides:
Y = a * Rb * Sc
ln(Y) = ln(a * Rb * Sc)
ln(Y) = ln(a) + b*ln(R) +c*ln(S)
This transforms the original equation into a linear equation.

Twenty-six observations are used to obtain the following regression results:
DEPENDENT VARIABLE: LNY R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 26 0.3647 4.21 0.0170
VARIABLE PARAMETER STANDARD T-RATIO P-VALUE
ESTIMATE ...

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