Question

True or False. Explain your answer:

d) Least squares estimates of the regression coefficients b0, b1, . . . bn are chosen to maximize R2 .

e) If all the explanatory variables are uncorrelated, the variance inflation factor (VIF) for each explanatory variable will be 1.

) b0 and b1 from a simple linear regression model are independent.

Answer #1

d) False, the least square estimates of the regression coefficients are not chosen, they are calculated from the provided data. The value of R2 depends on the variance of the residuals and the sample variance in the independent variables.

e) True, because when the explanatory variables are not correlated to each other then the variation inflation factor for each variable will be equal to 1. Variation inflation factor measures multicollinearity hence a zero value of correlation will have VIF equal to 1.

f) False, because b0 is calculated using b1.

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True or False: In the simple regression model, both ordinary
least squares (OLS) and Method of Moments estimators produce
identical estimates. Explain.

Answer true or false and state why.
1. The least-squares estimators are always BLUE and BUE.
2, In large samples the usually standardized ratios follow the
t-distribution.
3. If we rescale the dependent variable in regression by dividing
by 100, the new coefficient and their estimates will be multiplied
by 100.
4. In choosing between models we always seek to maximize
R^2.
(h) In choosing between models we always seek to maximize R2.
3

1) Which is NOT a fundamental assumption of OLS (Ordinary Least
Squares)?
a) The regression model is nonlinear
in the coefficients and error term.
b) Observations of the
error term are uncorrelated with each other.
c) No independent variable is a
perfect linear function of any other explanatory variables.
d) The error term has
homoscedasticity.
e) All independent variables will be uncorrelated
with the error term.
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2) You test a model that...

True or False: Please specify your reasons.
(i) If an independent variable in a multiple linear regression
model is an exact linear combination of other independent
variables, we can still calculate the least square estimators of
the intercept.
(ii) For the multiple linear regression y = β0 + β1x + β2x 2 +
u, β1 can be interpreted as the effect of one unit increase in x on
y.
(iii) In the multiple linear regression with an intercept, (the
sum...

23) Which of the following statements about collinearity in a
multiple regression model is FALSE? A).Collinearity should be
suspected if a model insignificant independent variables that are
supposed to be significant based on common sense. B).All
independent variables must be considered in determining
collinearity in a multiple regression model. C).The Variance
Inflation Factor can measure the collinearity of an independent
variable. D).Collinearity occurs when some of the independent
variables are related. E).Coefficients of independent variables
will not be affected by...

What are the pitfalls of simple linear regression? True or False
for each
Lacking an awareness of the assumptions of least squares
regression.
Not knowing how to evaluate the assumptions of least squares
regressions.
Not knowing the alternatives to least squares regression if a
particular assumption is violated.
Using a regression model without knowledge of the subject
matter.
Extrapolating outside the relevant range of the X and Y
variables.
Concluding that a significant relationship identified always
reflects a cause-and-effect relationship.

1. In a multiple
regression model, the following coefficients were obtained:
b0 = -10 b1
= 4.5 b2 = -6.0
a. Write the
equation of the estimated multiple regression model. (3 pts)
b Suppose a
sample of 25 observations produces this result, SSE = 480. What is
the estimated standard error of the estimate? (5 pts)
2. Consider the
following estimated sample regression equation:
Y = 12 + 6X1 -- 3 X2
Determine which of the following
statements are true,...

TRUE or FALSE and Explain why:
In a multiple regression model, the inclusion of a variable ?? ,
whose associated ?? = 0 in the population regression function, does
not bias the estimates of all the other slope parameters but can
increase their sampling variance.
Also, TRUE or FALSE and explain why:
It does not matter for the slope estimates if ?(?) ≠ 0 as long
as there is a constant term in the regression model.

6. True, False, Explain. Adding a variables to a regression that
are highly correlated with the independent variables already
included but not with the dependent variable will increase your
chance of committing type II errors when conducting tests of
statistical significance on the estimated coefficients.

Which of the following statements concerning regression and
correlation analysis is/are true?
A. If the correlation coefficient is zero, then there is no linear
relationship between the two variables.
B. A negative value for the correlation coefficient indicates that
high values of the independent variable are correlated with low
values of the dependent variable.
C. The slope coefficient for a simple linear regression model
measures the expected change in the independent variable for a unit
change in the dependent variable....

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