We use linear regression to find relationships
between two or more variables and to create a model that attempts to describe
the relationship.

A scatterplot is a 2-dimensional graph that displays
pairs of data (i.e. observations).

A correlation coefficient is a number that tells
strength and direction of a relationship.

·
0 means no linear relationship exists
(could be there is a curved relationship)

·
+1 or -1 means the points fall on a perfect
straight line

·
The closer the number is to +1 or -1,
the stronger the relationship.

·
Rule of thumb is that +0.7 or -0.7 (or more) is a strong relationship; +0.5 or
-0.5 indicates a moderate relationship.

Kinds of correlation coefficient – the one used
depends on the kind of data:

·
Pearson r – used for data measured at
least on an interval level (such my as data for TL, SL, and SV scales)

·
Spearman rho – used for linear
relationships when data is measured on an ordinal scale (such as a ranking)

·
Phi – used for linear relationships for
data measured dichotomously (e.g. yes/no, pass/fail)

·
also Point Biserial and Eta....don’t
care about these for now

For a null hypothesis, the expected correlation is 0. The key question is whether the variance from
what we expect can be attributed to a relationship that really exists, or is
the variance found only because of a sampling error.

A one-tailed hypothesis assumes the relationship is
positive or negative.

A two-tailed hypothesis makes no assumption about
the relationship.

For a correlational study, degrees of freedom =
N-2. One degree of freedom is lost for
every variable in the model. Degrees of
Freedom represents how many numbers are free to vary in a calculation sequence
(Steinberg, 2008).

References

Rumsey, D. (2009).

*Statistics II for Dummies*. Hoboken, NJ: Wiley Publishing, Inc.
Steinberg, W. J. (2008).

*Statistics Alive!*Thousand Oaks, CA: Sage Publications.
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