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DEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORY
DR. MOHAMMAD ABDUL MUKHYI, SE.,MM
DEMAND FOR A COMMODITYDEMAND FOR A COMMODITY
Permintaan adalah sejumlah barang yang
diminta oleh konsumen pada
tingkat harga tertentu.
Teori Permintaan adalah menghubungkan
antara tingkat harga dengan tingkat
kuantitas barang yang diminta pada
periode waktu tertentu.
Fungsi Permintaan: QdX = ƒ(Px, Py, Pz, I, T,
Tech, ….)
2
Hypothetical Industry Demand Curves
for New Domestic Automobiles at
Interest Rates of 6%, 8%, and 10%
Hypothetical Industry Demand Curves
for New Domestic Automobiles at
Interest Rates of 6%, 8%, and 10%
P
0 Q1
P P
Q2 Qx0 0
2 2 2
1 1 1
3 2 52 1 3
d1 d2 d3
Individual 1 Individual 2 Pasar
3
Permintaan Kentang di IndonesiaPermintaan Kentang di Indonesia
Permintaan kentang untuk periode 1980-2008:QdQdQdQdSSSS = 7.609 = 7.609 = 7.609 = 7.609 –––– 1.606P1.606P1.606P1.606PSSSS + 59N + 947I + 479P+ 59N + 947I + 479P+ 59N + 947I + 479P+ 59N + 947I + 479PWWWW + 271+ 271+ 271+ 271tttt....QdS = quantitas kentang yang dijual per tahun per
1.000 Kg.PS = harga kentang per kgN = rata-rata bergeral jumlah penduduk per 1 milyar.I = pendapatan disposibel per kapita penduduk.PW = harga ubi per kg yang diterima petani.T = trend waktu (t = 1 untuk tahun 1980 dan t = 2
untuk tahun 2008).
N = 150,73 I = 1,76 PW = 2,94 dan t = 1Bagaimana bentuk fungsi permintaan kentang?
Elastisitas Harga PermintaanElastisitas Harga Permintaan
Elastisitas Titik :
Elastisitas Busur :
Q
P x
P
Q
P/P
Q/Qd
hargaperubahan %
diminta yangjumlah perubahan %d
p
p
∂
∂=
∂
∂=
=
E
E
2/)QQ(
2/)PP( x
P
Q d
Q/n
P/n x
P
Q d
21
21p
p
+
+
∂
∂=
Σ
Σ
∂
∂=
E
atau
E
4
Elastisitas KumulatifElastisitas Kumulatif ::
Q
P x
P
Q d
Q/n
P/n x
P/N
Q/N d
p
p
Σ
Σ
∂Σ
∂Σ=
Σ
Σ
∂Σ
∂Σ=
E
atau
E
Elastisitas Silang :
Qx
Py x
Py
Qx
Py/Py)(
Qx/Qx)(c
Y barang hargaperubahan %
diminta yang X barangjumlah perubahan %c
xy
xy
∂
∂=
∂
∂=
=
E
atau
E
Elastisitas Pendapatan :
Qd
Y x
Y
Qd
Qd
Y x
Y
Qdy
pendapatanperubahan %
diminta yang barangperubahan % y
Σ
Σ
∂
∂=
∂
∂=
=
E
atau
E
Elastisitas Harga, Total Revenue, Marginal Revenue :
TR = P . Q
MR = ∆TR / ∆Q
+=
pE
1 1P MR
5
Q = 600 – 100P
Diminta :
a. Buat fungsi pendapatan.
b. Hitung nilai pendapatan marginal.
c. Bila P = 4 dan EP = -2 hitung MR
Jawab:
a. Q = 600 – 100P � P = 6 – Q/100
b. TR = P.Q � TR = (6 – Q/100).Q = 6Q –Q2/100
MR = 6 – Q/50
MR optimal = 0
0 = 6 – Q/50 � Q = 300
0
100
200
300
400
500
600
700
800
900
1000
0 200 400 600 800
output
TR ($)
TR
output
0
100
200
300
400500
600
700
800
900
1000
0 200 400 600 800
TR
($
)
D
MR = 6 – Q/50
TR = 6Q – Q2/100
Q = 600 – 100P
6
22
114
2
114 =
−=
−+=MR
Qx = 1,5 – 3,0Px + 0,8I + 2,0Py – 0,6Ps + 1,2A
Qx = penjualan kopi merek XPx = harga kopi merek XI = pendapatan disposibel per kapita per tahunPy = harga kopi pesaingPs = harga gula per kiloA = pengeluaran iklan untuk kopi merek X
Jika Px = 2; I = 2,5; Py = 1,8, Ps = 0.50 dan A = 1 berapa Q?
Qx = 1,5 – 3,0(2) + 0,8(2,5) + 2,0(1,8) – 0,6(0,50) + 1,2(1) = 2
6,02
12,1E
15,02
50,06,0E
8,12
8,12E
12
2,50,8 E
32
23E
A
XS
XY
I
P
=
=
−=
−=
=
=
=
=
−=
−=
Tingkat Elastisitas :
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SupplySupply
Penawaran adalah sejumlah barang yang
ditawarkan oleh produsen ke konsumen
pada tingkat harga tertentu.
Teori Penawaran adalah menghubungkan
antara tingkat harga dengan tingkat
kuantitas barang yang ditawarkan pada
periode waktu tertentu.
Fungsi Penawaran: QdX = ƒ(Px, Py, Pz, I, T,
Tech, ….)
Hypothetical Industry
Supply Curve for New
Domestic Automobiles
Hypothetical Industry
Supply Curve for New
Domestic Automobiles
8
Hypothetical Industry Supply Curves
for New Domestic Automobiles at
Interest Rates of 6%, 8%, and 10%
Hypothetical Industry Supply Curves
for New Domestic Automobiles at
Interest Rates of 6%, 8%, and 10%
Surplus, Shortage, and Market EquilibriumSurplus, Shortage, and Market Equilibrium
9
Comparative Statics of Changing DemandComparative Statics of Changing Demand
Comparative Statics of Changing SupplyComparative Statics of Changing Supply
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Comparative Statics of Changing Demand
and Changing Supply Conditions
Comparative Statics of Changing Demand
and Changing Supply Conditions
Demand and Supply Curves
Demand and Supply Curves
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Objectives
• Understand how regression analysis
and other techniques are used to estimate demand relationships
• Interpret the results of regression
models
– economic interpretation
– statistical interpretation and tests
• Describe special econometric problems
of demand estimation
Approaches to Demand Estimation
• 1. Surveys, simulated markets, clinics
Stated PreferenceRevealed Preference
• 2. Direct Market Experimentation
• 3. Regression Analysis
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A. Difficulties with Direct Market Experiments
(1) expensive and risky
(2) never a completely controlled experiment
(3) infeasible to try a large number of variations
(4) brief duration of experiment
(1) Specify variables: Quantity Demanded, Advertising,
Income, Price, Other prices, Quality, Previous
period demand, ...
(2) Obtain data: Cross sectional v. Time series
(3) Specify functional form of equation
Linear Yt = α + β X1t + γ X2t + ut
Multiplicative Yt = α X1tβ X2t
γ et
ln Yt = ln α + β ln X1t + γ ln X2t + ut
(4) Estimate parameters
(5) Interpret results: economic and statistical
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Violating the assumptions of regression including
(1) Multicollinearity- highly correlated independent
variables
(2) Heteroscedasticity- errors do not have the same
variance
(3) Serial correlation- error in period t is correlated with
error in period t + k
(4) Identification problems - data from interaction of
supply and demand do not trace out demand
relationship
Transit Example
• Y P T I H
• YEAR Riders Price Pop. Income Parking Rate
• 19661200 15 1800 2900 50
• 19671190 15 1790 3100 50
• 19681195 15 1780 3200 60
• 19691110 25 1778 3250 60
• 19701105 25 1750 3275 60
• 19711115 25 1740 3290 70
• 19721130 25 1725 4100 75
• 19731095 30 1725 4300 75
• 19741090 30 1720 4400 75
• 19751087 30 1705 4600 80
• 19761080 30 1710 4815 80
• 19771020 40 1700 5285 80
• 19781010 40 1695 5665 85
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• Y P T I H
• YEAR Riders Price Pop. Income Parking Rate
• 19791010 40 1695 5800 100
• 19801005 40 1690 5900 105
• 1981995 40 1630 5915 105
• 1982930 75 1640 6325 105
• 1983915 75 1635 6500 110
• 1984920 75 1630 6612 125
• 1985940 75 1620 6883 130
• 1986950 75 1615 7005 150
• 1987910 100 1605 7234 155
• 1988930 100 1590 7500 165
• 1989933 100 1595 7600 175
• 1990940 100 1590 7800 175
• 1991948 100 1600 8000 190
• 1992955 100 1610 8100 200
Linear Transit DemandLinear Transit DemandDependent Variable: RIDERS
Method: Least Squares
Date: 03/31/02 Time: 18:22
Sample: 1966 1992
Included observations: 27
Variable Coefficient Std. Error t-Statistic Prob.
C 85.43924 492.8046 0.173373 0.8639
PRICE -1.617484 0.495976 -3.26122 0.0036
POPULATION 0.643769 0.262358 2.453782 0.0225
INCOME -0.047475 0.012311 -3.85616 0.0009
PARKING 1.943791 0.349156 5.567113 0
R-squared 0.960015 Mean dependent var1026.222
Adjusted R-squared 0.952745 S.D. dependent var 94.25756
S.E. of regression 20.48984 Akaike info criterion 9.043312
Sum squared resid 9236.342 Schwarz criterion 9.283282
Log likelihood -117.0847 F-statistic 132.0525
Durbin-Watson stat 1.384853 Prob(F-statistic) 0
Riders = 85.4 – 1.62 price …
Pr Elas = -1.62(100/955) in 1992
15
Multiplicative Transit DemandMultiplicative Transit DemandDependent Variable: LRIDERS
Method: Least Squares
Date: 03/31/02 Time: 18:26
Sample: 1966 1992
Included observations: 27
Variable Coefficient Std. Error t-Statistic Prob.
C 3.24892 3.26874 0.993937 0.3311
LPRICE -0.13716 0.021873 -6.27052 0
LPOPULATION 0.613645 0.409148 1.49981 0.1479
LINCOME -0.13077 0.039913 -3.27646 0.0034
LPARKING 0.166443 0.032361 5.143338 0
R-squared 0.973859 Mean dependent var6.929651
Adjusted R-squared 0.969107 S.D. dependent var 0.09061
S.E. of regression 0.015926 Akaike info criterion -5.27614
Sum squared resid 0.00558 Schwarz criterion -5.03617
Log likelihood 76.22788 F-statistic 204.9006
Durbin-Watson stat 0.93017 Prob(F-statistic) 0
Ln Riders = exp(3.25)P-.14 …
MTB > Regress 'Y' 4 'P' 'T' 'I' 'H';
SUBC> Constant; SUBC> Residuals 'RESI1'; SUBC> DW.
The regression equation is Y = 85 - 1.62 P + 0.644
T - 0.0475 I + 1.94 H
Predictor Coef Stdev t-ratio p
Constant 85.4 492.8 0.17 0.864
P -1.6175 0.4960 -3.26 0.004
T 0.6438 0.2624 2.45 0.023
I -0.04747 0.01231 -3.86 0.001
H 1.9438 0.3492 5.57 0.000
s = 20.49 R-sq = 96.0% R-sq(adj) = 95.3%
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Analysis of Variance
SOURCE DF SS MS F p
Regression 4 221760 55440 132.05 0.000
Error 22 9236 420
Total 26 230997
Durbin-Watson statistic = 1.38
Ch 3: DEMAND ESTIMATIONCh 3: DEMAND ESTIMATION
In planning and in making policy decisions, managers must have some idea about the characteristics of the demand for their product(s) in order to attain the objectives of the firm or even to enable the firm to survive.
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Demand information about customer sensitivity toDemand information about customer sensitivity to
�modifications in price
�advertising
�packaging
�product innovations
�economic conditions etc.
are needed for product-development strategy
• For competitive strategy details about customer
reactions to changes in competitor prices and the quality of competing products play a significant role
What Do Customers Want?What Do Customers Want?
• How would you try to find out customer behavior?
• How can actual demand curves be estimated?
18
From Theory to PracticeFrom Theory to Practice
D: Qx = f(px, Y, ps, pc, Τ, N)
(px=price of good x, Y=income, ps=price of substitute,
pc=price of complement, Τ=preferences, N=number of consumers)
• What is the true quantitative relationship between demand and the factors that affect it?
• How can demand functions be estimated?
• How can managers interpret and use these
estimations?
Most common methods used are:Most common methods used are:
a) consumer interviews or surveys
� to estimate the demand for new products
� to test customers reactions to changes in the price or advertising
� to test commitment for established products
b) market studies and experiments
� to test new or improved products in controlled settings
c) regression analysis
� uses historical data to estimate demand functions
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Consumer Interviews (Surveys)Consumer Interviews (Surveys)
• Ask potential buyers how much of the
commodity they would buy at different
prices (or with alternative values for the non-price determinants of demand)
�face to face approach
�telephone interviews
Consumer Interviews cont’dConsumer Interviews cont’d
• Problems:
– Selection of a representative sample
• what is a good sample?
– Response bias
• how truthful can they be?
– Inability or unwillingness of the respondent to answer accurately
20
Market Studies and ExperimentsMarket Studies and Experiments
• More expensive and difficult technique
for estimating demand and demand
elasticity is the controlled market study or experiment
– Displaying the products in several different stores, generally in areas with different characteristics, over a period of time
• for instance, changing the price, holding everything else constant
Market Studies and Experiments cont’dMarket Studies and Experiments cont’d
• Experiments in laboratory or field
– a compromise between market studies and surveys
– volunteers are paid to stimulate buying conditions
21
Market Studies and Experiments cont’dMarket Studies and Experiments cont’d
• Problems in conducting market studies
and experiments:
a) expensive
b) availability of subjects
c) do subjects relate to the problem, do they take them seriously?
BUT: today information on market
behavior also collected by membership
and award cards
Regression Analysis and Demand EstimationRegression Analysis and Demand Estimation
• A frequently used statistical technique in demand estimation
• Estimates the quantitative relationship between the dependent variable and independent variable(s)
�quantity demanded being the dependentvariable
�if only one independent variable (predictor) used: simple regression
�if several independent variables used:
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A Linear Regression ModelA Linear Regression Model
• In practice the dependence of one variable on another might take any number of forms, but an assumption of linear dependency will often provide an adequate approximation to the true relationship
Think of a demand function of general form:Think of a demand function of general form:
Qi = α + β1Y - β2 pi + β3ps - β4pc + β5Z + ε
where
Qi = quantity demanded of good i
Y = incomepi = price of good ips = price of substitute(s)pc = price of complement(s)Z = other relevant determinant(s) of demand
ε = error term
Values of α and βi ?
23
α and βi have to be estimated from historical dataα and βi have to be estimated from historical data
• Data used in regression analysis
�cross-sectional data provide information on variables for a given period of time
�time series data give information about variables over a number of periods of time
• New technologies are currently
dramatically changing the possibilities of
data collection
Simple Linear Regression ModelSimple Linear Regression Model
In the simplest case, the dependent variable Y is assumed to have the following relationship with the independent variable X:
Y = α + βX + εwhere
Y = dependent variableX = independent variable
α = intercept
β = slope
ε = random factor
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Estimating the Regression EquationEstimating the Regression Equation
• Finding a line that “best fits” the data– The line that best fits a collection of X,Y
data points, is the line minimizing the sum of the squared distances from the points to the line as measured in the vertical direction
– This line is known as a regression line, and the equation is called a regression equation
Estimated Regression Line:XY βα +=ˆ
Observed Combinations of Output and Labor input
Observed Combinations of Output and Labor input
Skatter Plot
0
100
200
300
400
500
600
0 100 200 300 400 500 600 700 800
L
Q
L
Q
YY −ˆ
25
Regression with ExcelRegression with Excel
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,959701
R Square 0,921026
Adjusted R Square0,917265
Standard Error47,64577
Observations 23
ANOVA
df SS MS F Significance F
Regression 1 555973,1 555973,1 244,9092 4,74E-13
Residual 21 47672,52 2270,12
Total 22 603645,7
CoefficientsStandard Errort Stat P-value Lower 95%Upper 95%Lower 95,0%Upper 95,0%
Intercept -75,6948 31,64911 -2,39169 0,026208 -141,513 -9,87686 -141,513 -9,87686
X Variable 11,377832 0,088043 15,64957 4,74E-13 1,194737 1,560927 1,194737 1,560927
Evaluate statistical significance of regression coefficients using t-test and statistical significance of R2 using F-test
Statistical analysis is testing hypothesesStatistical analysis is testing hypotheses
• Statistics is based on testing hypotheses
• ”null” hypothesis = ”no effect”
• Assume a distribution for the data,
calculate the test statistic, and check the
probability of getting a larger test
statistic value
σ
µ−=
XZ
Z For the normal distribution:
p
26
t-test: test of statistical significance of each estimated regression coefficient
t-test: test of statistical significance of each estimated regression coefficient
• βi = estimated coefficient
• H0: βi = 0
• SEβ: standard error of the estimated
coefficient
• Rule of 2: if absolute value of t is greater than 2, estimated coefficient is significant at the 5% level (= p-value < 0.05)
• If coefficient passes t-test, the variable
iSE
t i
β
β=
Sum of SquaresSum of Squares
27
Sum of Squares cont’dSum of Squares cont’d
TSS = Σ(Yi - Y)2
(total variability of the dependent variable about its mean Y)
RSS = Σ(Ŷi - Y)2
(variability in Y explained by the sample regression)
ESS = Σ(Yi - Ŷi)2
(variability in Yi unexplained by the dependent variable x)
This regression line gives the minimum ESS among all possible straight lines.
The Coefficient of DeterminationThe Coefficient of Determination
• Coefficient of determination R2
measures how well the line fits the scatter plot (Goodness of Fit)
�R2 is always between 0 and 1
�If it’s near 1 it means that the regression line is a good fit to the data
�Another interpretation: the percentage
TSS
ESS1
TSS
RSSR
2 −−−−========
28
F-testF-test
• The null hyphotesis in the F-test is
H0: β1= 0, β2= 0, β3= 0, …
• F-test tells you whether the model as a whole explains variation in the dependent variable
• No rule of thumb, because the values of the F-distribution vary a lot dependingon the degrees of freedom (# of variables vs. # of observations)– Look at p-value (”significance F”)
Special Cases:Special Cases:
• Proxy variables
– to present some other “real” variable, such as taste
or preference, which is difficult to measure
• Dummy variables (X1= 0; X2= 1)
– for qualitative variable, such as gender or location
• Linear vs. non-linear relationship
– quadratic terms or logarithms can be used
Y = a + bX1 + cX12
QD=aIb ⇒ logQD= loga + blogI
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Example: Specifying the Regression Equation for Pizza DemandExample: Specifying the Regression Equation for Pizza Demand
We want to estimate the demand for pizza among college students in USA
�What variables would most likely affect their demand for pizza?
�What kind of data to collect?
Data: Suppose we have obtained cross-sectional data on randomly selected
30 college campuses (through a survey)
Data: Suppose we have obtained cross-sectional data on randomly selected
30 college campuses (through a survey)
The following information is available:
�average number of slices consumed per month by students
�average price of a slice of pizza sold around the campus
�price of its complementary product (soft drink)
�tuition fee (as proxy for income)
�location of the campus (dummy variable is included to find out whether the demand for pizza is affected by the number of available substitutes); 1 urban, 0 for non-
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Linear additive regression line:Linear additive regression line:
Y = a + b1pp + b2 ps + b3T + b4L
where
Y = quantity of pizza demanded
a = the intercept
Pp = price of pizza
Ps= price of soft drink
T = tuition fee
L = location
bi = coefficients of the X variables measuring the impact of the variables on the demand
for pizza
Estimating and Interpreting the Regression
Coefficients
Estimating and Interpreting the Regression
Coefficients
Y = 26.27- 0.088pp - 0.076ps + 0.138T- 0.544L
(0.018) (0.018)* (0.020)* (0.087) (0.884)
R2 = 0.717
adjusted R2 = 0.67F = 15.8
Numbers in parentheses are standard errors of coefficients.
31
Problems in the Use of Regression Analysis:Problems in the Use of Regression Analysis:
• identification problem
• multicollinearity
(correlation of coefficients)
• autocorrelation
(Durbin-Watson test)
• normality assumption fails
(outside the scope of this course)
Identification ProblemIdentification Problem
• Can arise when all effects on Y are not
accounted for by the predictors
Q
P
Q
P S
D3D2
D1
Can demand be upward sloping?!
OR…?
D?!
32
MulticollinearityMulticollinearity
• A significant problem in multiple
regression which occurs when there is a
very high correlation between some of the predictor variables.
Resulting problem:Resulting problem:
Regression coefficients may be very
misleading or meaningless because…
– their values are sensitive to small changes in the data or to adding additional observations
– they may even be opposite in sign from what ”makes sense”
– their t-value (and the standard error) may change a lot depending upon which other predictors are in the model
33
Multicollinearity cont’dMulticollinearity cont’d
Solution:
Don’t use two predictors which are very
highly correlated (however, x and x2 are
O.K.)
Not a major problem if we are only trying
to fit the data and make predictions and
we are not interested in interpreting the numerical values of the individual
regression coefficients.
Multicollinearity cont’dMulticollinearity cont’d
• One way to detect the presence of multicollinearity is to examine the correlation matrix of the predictor variables. If a pair of these have a high correlation they both should not be in the regression equation – delete one.
1.00.91-.59.86X3
.911.00-.82.81X2
-.59-.821.00-.45X1
.86.81-.451.00Y
X3X2X1YCorrelation Matrix
34
AutocorrelationAutocorrelation
• Correlation between consecutive
observations
• Usually encountered with time series data
– E.g. seasonal variation in demand
time
D � Creates a problem with t-tests: insignificant variables may appear significant
A test for Autocorrelated Errors:DURBIN-WATSON TEST
A test for Autocorrelated Errors:DURBIN-WATSON TEST
• A statistical test for the presence of autocorrelation
• Fit the time series with a regression model and then determine the residuals:
ttt yy ˆ−=ε
∑
∑
=
=
−−
=n
t
t
n
t
tt
d
1
2
2
2
1)(
ε
εε
35
The Interpretation of d:The Interpretation of d:
The Durbin-Watson value d will always be
0 ≤ d ≤ 4
40 2
No correlation
Strong negative correlation
Strong positive correlation
Multiple Regression ProcedureMultiple Regression Procedure
1. Determine the appropriate predictors and the form of the regression model
– Linear relationship
– No multicollinearity
– Variables ”make sense”
2. Estimate the unknown α and β coefficients
3. Check the “goodness” of the model (R2,
global F-test, individual t-test for each βcoefficient)
4. Use the fitted model for predictions (and determine their accuracy)
36
Additional Comments:Additional Comments:
• OCCAM’S RAZOR. We want a model
that does a good job of fitting the data
using a minimum number of predictors. A high R2 is not the only goal; variables
used should be ”meaningful”
• Don’t use more predictors in a
regression model than 5% to 10% of n
• Correlation is not causality!
FORECASTINGFORECASTING
• Expert opinion –based methods
– Delphi method
• Data-based methods
– Time series analysis
• History can predict the future?
– Regression analysis
• Forecast the values of the Xi’s to get Y
• Assumes the relationship between Xi’s and Y
does not change