4) What are the range of the RHS value of the constraints such that the shadow prices are
valid?
437.78
< Peanuts <
660.00
185.00
< Cashews <
253.00
80.00
< Almonds <
Inf
57.14
< Walnuts <
100.00
0 (-Inf)
< Plain vs Premium <
375.00
Hypothesis testing: t-test
I
General Procedure
I
Step 1: Write down H0 and H1 in terms of s, xs and y s (express
H0 and H1 in mathematical language). Determine the rejection
region based on H1 .
I
Step 2: Get point estimate of what you are testing, i.e. r
Formula
Use formula in calculation
Least Squares Expressions Useful for Theory
172 = 52 + 21mg,-
x.- 3
1' =
2(1, if
2,.- = 0, 2W,- =1, M = um.- rc)2
Properties of the Least Squares Estimators
var 1 =02 2 var
(b ) [N2(x:7r)l (b2)
20: .7):
Estimated Error
Compute the Standard Error
I
Always write down the expression you want to compute the standard
error for as a function of bs (plug in other values, i.e. the given
value of xs).
I
You should remember that in this course only bs are random
variables, and xs
Marginal Eect and Elasticity
Example: Interpretation of Log-linear Model With Indicator Variable
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Percentage change:
I
I
Approximate calculation: 100% (log y1
Exact calculation:100% expcfw_log y1
log y0 )
log y0
Outline
I
Regression Model Basics
I
Assumptions, Formula, Interpretations, Rescaling, Marginal Eects
and Elasticities
I
Inference
I
Estimation, Standard Error, Confidence Interval, t-test, F-test, and
Prediction
I
Evaluating Models
I
Goodness of Fit, Poss
Hypothesis testing: t-test
I
Typical Questions in Hypothesis Testing
I
Test one coefficient: see part (a) in 3.8
I
Test marginal eect or slope: see part (d) in 3.8.
I
Test the expected value at some point: see part (b) in 3.8.
Confidence Interval
I
General Procedure
I
Step 1: Get point estimate of what you want to construct an
interval for.
I
Step 2: Get standard error of what you want to construct an interval
for.
I
Step 3: Get critical t-value, t1
I
Step 4: (1-)% CI: point es
Answer Report:
Sensitivity Report:
From the answer report, the red box shows the change in the objective function value:
Final Value- Original Value= 0.768-0.78= -0.012 Which is minus the value of the shadow
price of protein.
Questions 1-4 are all solved
.
1.4 Relax the RHS value of the protein constraint by 1 unit (i.e., reduce the protein
requirement by 1 unit), solve the optimal solution again using Excel Solver. What is
the change in the objective function value? Copy and paste the new Answer and
Sens
Prediction
Forecast error at x = x0
The forecast error is se(f ) =
A (1
r
h
2 1 +
1
N
)100% prediction interval for y0 is
y se(f )tc
.
+
(x0 x)2
P
(xi x)2
i
Model Selection
I
R 2 : the higher, the better (to some extent)
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Interpretation: the proportion of variation in y explained by the
explanatory variables
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Use when comparing models with the same number of xs and the
same y
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Adjusted R 2 : the higher, th
In this problem, we expect the shadow price to change since we are taking the RHS
OUTSIDE the validity range. In this case the constraint becomes non-binding and the
shadow price becomes zero.
Problem 5 - 7:
Formulate each LP problem and solve it in Excel
4) What are the range of the RHS value of the constraints such that the shadow prices are
valid?
0 (-Inf)
< Nutrient A needed <
80
56
< Nutrient B needed <
Inf
6.4
< Nutrient C needed <
40
0 (-Inf)
< Nutrient D needed <
224
0
< Feed Z max <
2) Print the answer report. What are the optimal solutions? What are the sensitivity range
of the objective function coefficients such that the optimal solutions stay the same?
What are the optimal solutions?
Objective Cell (Max)
Cell
Name
$E$5 Profit
Ori
Problem 7: Party Mix Problem 2-42 on page 61.
1) Write the LP formulation, specify the objective function and the constraints.
Let > : # , H : # , N : #
= . + . + .
st:
0.8> + 0.5H 500
0.2> + 0.3H + 0.3N 225
0.1H + 0.4N 80
0.1H + 0.4N 80
> 2N
Z 0
Upper bound for Coefficient of feed A: Obj. Coefficient +Allowable increase=
0.1+0.1=0.2
Lower bound for Coefficient of feed A: Obj. Coef. +Allowable Decrease=0.10.025=0.075
2.2 Copy and paste the Sensitivity Report below. What is the shadow price of the
Confidence Interval
I
Typical Questions in Constructing Confidence Interval
I
CI for
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CI for marginal eect or elasticity
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CI for y at some point of x when the dependent variable is ln y
Note: Compare confidence interval with prediction interval; they ar
See the above figure. Initially, the quantity of Ph.D.s is relatively fixed. The increased demand raises their
salary. In the long run, the increased salary attracts more people to train for a Ph.D. in English literature.
The long-run elasticity of supply
63) Suppose that the long-run world demand and supply elasticities of crude oil are -0.906 and 0.515,
respectively. The current long-run equilibrium price is $30 per barrel and the equilibrium quantity is 16.88
billion barrels per year.
a. Derive the (lin
2.7 Quantity Supplied Need Not Equal Quantity Demanded
1) Municipalities that have adopted the policy of "rent control" typically set the rentals on certain
apartments well below equilibrium. As a result,
A) landlords have a difficult time finding tenants
Solutions to HW 3
1. Set up in Excel:
1.1 Copy and paste the Answer report below, and interpret the meaning of the
sensitivity range for cost of Brand A and Brand B.
Note that this question only asks you to paste the Answer report, however the sensitivity
Status: Old
12) If the government decides to levy an ad valorem tax on product with a perfectly inelastic supply. The
consumers tax incidence will be
A) 0.
B) 1.
C) .5.
D) Cannot be determined.
Answer: A
Topic: Effects of a Sales Tax
Status: Old
13) In th