Question

- If the errors in the CLR model are not normally distributed, although the OLS estimator is no longer BLUE, it is still unbiased.
- In the CLR model, β
^{OLS}is biased if explanatory variables are endogenous. - The value of R
^{2}in a multiple regression cannot be high if all the estimates of the regression coefficients are shown to be insignificantly different from zero based on individual*t*tests. - Suppose the CNLR applies to a simple linear regression y =
β
_{1}+ X_{2}β_{2}+ ε, and you obtained the OLS results 0.73 with standard error 0.2 from a data set. Since β_{2}^{OLS}is unbiased, the sampling distribution of β_{2}^{OLS}is distributed around 0.73 with standard error 0.2. - In the CLR model,
**y = X**_{1}**β**(population) and_{1}+ X_{2}β_{2}+ ε**y = X**_{1}**β**_{1}^{OLS}**+ X**_{2}β_{2}^{OLS}**+****e**(sample),**β**_{2}can be obtained when the residuals from a regression of^{OLS}**y**on**X**alone are regressed on the set of residuals obtained when each column of_{1}**X**is regressed on_{2}**X**._{1}

Answer #1

Statement 1 is true as normality plays no role in unbiasedness.Normality is required only to derive distribution of OLS estimators.

Statement 2 is true that OLS estimator are biased if explanatory variables are endogeneous.

Statement 3 is False as in case of muticollinearity
R^{2} can be high even when coefficient are
insignificant

Statement 4 is False as sampling distribution of
β_{2}^{OLS} is distributed around its
expected value i.e β_{2} and not a particular sample value
of β_{2}^{OLS}

Statement 5 is correct. Because in this process we are purifying
Y and X_{2} of the influence of X_{1.}Here
residuals indicate their purified value on which simple regression
model can be applied.

Suppose y is determined by the true model
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n (total observations) = 41
Significance level = 0.05 = 5%
Variable Parameter Estimate Std. Error of
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df
SS
MS
F
Significance
F
Regression
2
2.12E+12
1.06E+12
55.978
3.31E-08
Residual
17
3.11E+11
1.90E+10
Total
19
2.46E+12
Coefficients
Standard
Error
t
Stat
p-value
Lower 95%
Upper 95%
Intercept
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130,984
−7.534
0.000
−1,263,244
−710,540
x1
28,968
32,080
0.903
0.379
−38,715
96,651
x2
30,888
32,925
0.938
0.362
−38,578
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t-statistics
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68.90
Crude Oil
0.0651
32.89
S&P 500
-0.0020
18.09
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-0.0415
14.20
PDI
0.0001
17.32
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1.
Management of a fast-food chain proposed the following
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β1x1 +
β2x2 +
β3x3 +
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Summary of Fit
RSquare
0.956255
RSquare Adj
0.951207
Root Mean Square Error
0.240340
Mean of Response
8.382667
Observations (or Sum Wgts)
30
Analysis of Variance
Source
df
Sum...

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