Question

How is a linear relationship between two variables measured in statistics? Explain.

Answer #1

**Answer:**

**The linear relationship
between two variable is measured using Coefficient of Correlation,
r given as:**

** **

**The correlation coefficient,
r is a numerical measure that measures the strength and direction
of a linear relationship between two quantitative variables which
ranges from -1 to 1. The closer the value of r gets to 1 or -1, the
stronger the relationship between the two variables.**

**If r is positive then there exists positive linear relationship between X and Y i.e. as X increases Y also increases and vice versa.****If r is negative then there exists negative linear relationship between X and Y i.e. as X increases Y decreases and vice versa.**

Explain the importance of linearity when measuring the
relationship between two continuous variables. If the relationship
is not linear, what test would be advisable? List and explain two
continuous variables that are unlikely to have a linear
relationship.

The strength of the relationship between two quantitative
variables can be measured by
the y-intercept of the simple linear regression
equation.
the slope of a simple linear regression equation.
both the coefficient of correlation and the coefficient of
determination.
the coefficient of determination.
the coefficient of correlation.

Chose a relationship between two variables that can be shown
with a non-linear function (and is not an example from the notes).
Name the functional form used, give the general formula used,
sketch the graph and BRIEFLY explain your choice.

Correlation is a visual method for determining the relationship
between two variables... including linear, curve linear, strong,
weak, positive, negative, and no relationships. The correlation
coefficient is a mathematical reflection of that relationship.
Regression analysis is the same thing as the correlation
coefficient. True or False

Which of the following correlations indicates the strongest
linear relationship between two variables?
0.75
- 0.90 (is it right answer?)
0.50
1.25

The covariance and correlation coefficient are measures that
quantify the non-linear relationship between two variables.
T/F

When understanding the linear relationship between two continuous
variables, what does the intercept tell us?

In each example, explain whether there is a significant linear
correlation between the two variables, and determine what
proportion of the variation can be explained by the linear
association between the variables: Linear correlation coefficient
between bear chest size and weight is 0.993, N = 21 Linear
correlation coefficient between the number of registered automatic
weapons and the murder rate is 0.885, N = 1000 Linear correlation
coefficient between the weight in female subjects and the BMI
metric is 0.936,...

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...

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...

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