Question

In a multiple regression, why is the estimated correlation between the coefficients beta 1 hat and beta 2 hat positive when the correlation between the regressors is negative?

Answer #1

The beta values, or b coefficients, are estimates of the
parameters of the straight line equation underlying your data set.
The **absolute** **value** of the
correlation coefficient is a measure of the alignment of the points
in your data set. The sign of the coefficient indicates whether the
slope of the fitted line is positive or negative.

We take absolute value because of this the estimated correlation between the coefficients beta 1 hat and beta 2 hat positive when the correlation between the regressors is negative

Match the following
sample correlation coefficients with the explanation of what that
correlation coefficient means. Type the correct letter in each
box.
1. ?= −.15
2. ?= .92
3. ?= −.97
4. r= -1
The regression line is the straight line that bests fits a set
of data points according to what?
A. Most accurate regression criterion
B. Least-squares criterion.
C. Greatest-squares criterion
D. None of the above
4. ?=−1
A. a strong negative relationship between ? and
?
B....

A negative serial correlation exists when a _______________
error is followed by a _______________ error.
Multiple Choice
positive, negative
negative, positive
negative, negative
positive, positive
Which one of the following correctly explains the difference
between a trend model and a causal model?
Multiple Choice
A trend model tracks the past time trend and projects it forward
while the causal model looks at a change in an independent variable
that causes a change in a dependent variable.
A trend model identifies...

Which of the following statements are true of correlation
coefficients?
Group of answer choices
The more negative the number is, the weaker the
relationship.
A correlation coefficient of -0.90 indicates that there is an
inconsistent relationship between the variables.
The closer the coefficient is to 1 or -1, the weaker the
relationship.
A correlation coefficient of 0.05 indicates that there is an
inconsistent relationship between the variables.
Which type of analysis is more flexible than an
independent-samples t-test and allows...

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,...

when the highest partial correlation coefficient is significant at
any step in stepwise multiple regression, what does this tell us
about R^2 change?

1.What is the relationship between covariance
analysis, correlation analysis and linear regression
analysis?
2. What is the difference between covariance, correlation and
linear regression analysis?

Explain why a multiple regression analysis reported an F
statistic with a p < 0.05 but none of the individual
coefficients were significant.

Regression Statistics
Multiple
R
0.710723
R
Square
0.505127
Adjusted
R Square
0.450141
Standard
Error
1.216847
Observations
21
ANOVA
df
SS
MS
F
Significance F
Regression
2
27.20518
13.60259
9.186487
0.00178
Residual
18
26.65291
1.480717
Total
20
53.8581
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
58.74307
12.66908
4.636728
0.000205
32.12632
85.35982
32.12632
85.35982
High
School Grad
-0.00133
0.000311
-4.28236
0.000448
-0.00198
-0.00068
-0.00198
-0.00068
Bachelor's
-0.00016
5.46E-05
-3.00144
0.007661
-0.00028
-4.9E-05
-0.00028
-4.9E-05...

What are the requirements of the least-squares regression
model?
What is a correlation matrix?
How can you use technology to find a multiple regression
equation?
Why is it important to perform graphical as well as analytical
analyses when analyzing relations between two quantitative
variables?

6. Consider the following sample regression
results:
Y hat = 15.4 + 2.20 X1 +
48.14
X2
R2 = .355
(6.14)
(.42)
(5.21)
n = 27
The numbers in the parentheses are the estimated standard errors
of the sample regression coefficients.
6. (continued)
a. Construct a 95% confidence interval for
b1.
b. Is there evidence of a linear relationship
between X2 and Y at the 5% level of
significance?
c. If you were to use a global test...

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