Question

Suppose we have a regression model with 3 independent variables
and an R^{2} value of 0.65 and an adjusted R^{2}
value of 0.61. When we add a fourth independent variable, the new
R^{2} value is 0.73 and the new adjusted R^{2}
value is 0.54. What can we conclude about this newly added
independent variable?

Group of answer choices

The new independent variable improves our model because R-squared increased

The new independent variable improves our model because the adjusted R-squared value decreases

The new independent variable may be unnecessary because the adjusted R-squared value decreases

None of the above

Answer #1

1. If we add k indicator variables to a regression model for a
categorical variable with k levels, the regression tool will return
one coefficient estimate of 0.00 because:
a. The k variables are not independent b. The k variables are
independent
2. If we add up to 3rd order polynomial terms to a regression
model (e.g., x, x^2 and x^3) it will allow the relationship between
X and Y to change direction 3 times.
a. True b. False
3....

With a multi-variable linear regression model how can we decide
which independent variables to remove from the model?

(2)
The following are regression results
for the model with five independent variables.
PREDICTOR COEF STDEV
Constant -19.672 5.422
OUTLETS -0.00063 0.00264
CARS 1.7399 0.5530
INCOME 0.4099 0.04385
AGE 2.0357 0.8779
BOSSES -0.0344 0.1880
SSRegression = 1593.
81 SS
(total) = 1602.89
b. What percent
of the variation in sales does the regression equation explain? (5
pts)
99.43%
c. Conduct a
global test to determine if ANY of the independent variables are
linearly related to annual sales. Use alpha = .01. (16
pts)
d. What
variables would you consider eliminating from this model? Why? Seat
of the pants guesses...

A sample of 10 observations collected in a regression study on
three variables, x_1(independent variable), x_2(independent
variable and y(dependent variable). The sample resulted in the
following data.
SSR=28, SST=34
Using a 0.01 level of significance, we conclude that the regression
model is significant overall. (Enter 1 if the conclusion is
correct. Enter 0 if the conclusion is wrong.)

The following results were obtained as part of a multiple
regression analysis involving 3 independent variables:
SSR = 11440 SSYY = 16781
and n = 28
What is the value of the calculated F statistic?
What is the critical value for the model test if alpha =
0.05?
What is the value of the coefficient of determination?
What is the value of the standard error of the estimate?
What is the value of adjusted R2?
What are the total number...

A regression model involved 5 independent variables and 126
observations. The critical value of t for testing the
significance of each of the independent variable's coefficients
will have is __

A regression model involved 5 independent variables and 136
observations. The critical value of t for testing the
significance of each of the independent variable's coefficients
will have

Problem 7
You estimated a regression model using annual returns of
ExxonMobil (as a dependent variable) and of the market (as an
independent variable). The R-squared of this regression is 0.9. We
can conclude that:
A) ExxonMobil’s systematic risk is higher than ExxonMobil’s
unsystematic risk
B) ExxonMobil’s unsystematic risk is higher than ExxonMobil’s
systematic risk
C) ExxonMobil’s systematic risk and ExxonMobil’s unsystematic
risk are about the same
D) This R-squared implies that ExxonMobil’s beta is larger than
one
E) This...

Suppose we estimate a regression model containing a
constant term and two explanatory variables. The analysis is based
on a sample size of 25 and produces a Durbin Watson statistic
d=1.85.
a. Approximately, what is the correlation coefficient
between consecutive error terms?
b. If this model has an R2 = .75, what is the value of
the CALCULATED F statistic associated with a GLOBAL
test?
c. At the 1% level what is the CRITICAL value associated
with a global test...

estimate std.error
Intercept 26184.4 3517.3
snowfall 3824.8 247.5
r^2=.8565
adjusted r^2= .8529
s=8991
For each additional inch of snowfall, steam runoff
decreases by 26,184 acre-feet, on average.
increases by 26,184 acre-feet, on average.
.decreases by 3824 acre-feet, on average.
increases by 3824 acre-feet, on average
If multicollinearity is present, then we can conclude that the
fitted regression model:
may have estimated slopes very different from what we should
expect due to numerical instabilities, making correct
interpretation of the effect on...

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