Question

Explain why for statistical inference for linear regression and correlation, we perform the inference of the slope of the regression line. Also, why is a null value of 0 considered to be no relationship between the variables? Lastly, how does this relate to 0 being in the confidence interval for the slope of the regression line?

Answer #1

If you have any doubt, please ask in the comment section

Which of the following statements concerning the linear
correlation coefficient are true?
I: If the linear correlation coefficient for two variables is
zero, then there is no relationship between the variables.
II: If the slope of the regression line is negative, then the
linear correlation coefficient less than one.
III: The value of the linear correlation coefficient always lies
between -1 and 1.
IV: A linear correlation coefficient of 0.62 suggests a stronger
linear relationship than a linear correlation coefficient...

1) Regression:
a) is a statistical technique that is not influenced by
outliers.
b) identifies the resistance of a relationship.
c) measures the strength but not the direction of a
relationship.
d) can be used for prediction.
2) The best-fitting regression line:
a) has the smallest total standard error.
b) has the smallest slope.
c) has the largest total squared error of prediction.
d) is the line with the smallest (Y – Ŷ)2 value.
If the slope (b) of the...

Which of the following statements concerning the linear
correlation coefficient is/are true?
A: If the linear correlation coefficient for two variables is zero,
then there is no relationship between the variables.
B: If the slope of the regression equation is negative, then the
linear correlation coefficient is negative.
C: The value of the linear correlation coefficient always lies
between -1 and 1 inclusive.
D: A correlation coefficient of 0.62 suggests a stronger linear
relationship than a correlation coefficient of -0.82.

Discussion 1: Searching for Causes
This week examines how
to use correlation and simple linear regression to test the
relationship of two variables. In both of these tests you can use
the data points in a scatterplot to draw a line of best fit; the
closer to the line the points are the stronger the association
between variables. It is important to recognize, however, that even
the strongest correlation cannot prove causation.
For this Discussion,
review this week’s Learning Resources...

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....

Concept Questions
We've discussed that a linear regression assumes the
relationship between variables is linear: it forms a constant
slope. But suppose the data is U-shaped or inverted U-shaped. How
would you created a linear regression so the line would follow this
data? (hint: think of what the equation for a U-shaped line looks
like.)
Suppose you applied a scalar to a variable. Then you used both
the original variable and the scaled variable as explanatory
variables. What would happen...

a. If r is a negative number, then b (in the line of regression
) is negative.
true or false
b.The line of regression is use to predict the theoric average
value of y that we expect to occur when we know the value of x.
true or false
c. We can predict no matter the strength of the correlation
coefficient.
true or false
d. The set of all possible values of r is, {r: -1< r <
1
treu...

Please answer the question briefly and
clearly.
1. The best model to describe a linear relationship between two
variables is the _______.
2. An assumption of linear regression states that for each value
of X, there is a group of Y values that are
statistically (Independent) and (normally
distributed) about the regression line.
3. If the slope of a regression line is zero, the orientation of
the regression line is (Flat, or Constant), which
indicates a lack of a relationship....

a correlation of 0.03 is considered to be a null one
true or false
an strong correlation between two variables establishes a cause
and effect relationship between them
true or false
a positive correlation is also known as direct
true or false
if r=1 then all points in the scatter diagram are over the line
of regression
true or false

Which statement explains why correlation could be 0 even if a
strong relationship between two variables existed?
Group of answer choices
Since the correlation is 0, there is no strong relationship
between the two variables; and a scatterplot would be
misleading.
Correlation can be 0 even if there is a strong linear
relationship between the variables.
Correlation only measures the strength of the relationship
between two variables when the units of the two variables are the
same.
Correlation does not...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 11 minutes ago

asked 13 minutes ago

asked 17 minutes ago

asked 23 minutes ago

asked 25 minutes ago

asked 37 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago