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CORRELATION AND REGRESSION
Correlation and Regression
Karli Bryant
BUSI 820 Quantitative Research Methods
December 1st, 2023
Discussion Board 6
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CORRELATION AND REGRESSION
Correlation and Regression
D6.8.1 – Why would we graph scatterplots and regression lines?
Graphing scatterplots and regression lines provides the researcher with more insight into
the data being analyzed. One of the primary reasons it is important to take this step is to check
for any violations. The Pearson correlation in addition to the regression statistic assumes a linear
relationship and therefore reviewing the scatterplot lines allows the researcher to see if there are
any violations of linearity whereas in reviewing regression lines the data can often be explained
more accurately (Morgan, Barrett, Leech & Gloeckner, 2022). Essentially, most graphs, and
especially graphs reflecting scatterplots and regression lines, allow for any type of outliers to be
more easily seen by the researcher.
D6.8.2 – In Output 8.2, (a) what do the correlation coefficients tell us?
In output 8.2, the correlation coefficient is .34 and is a measurement of the strength of
association. When utilizing the correlation coefficient, effect sizes have an absolute value of less
than 1.0 and will vary between -1.0 and +1.0 with 0 being no effect (Morgan, Barrett, Leech &
Gloeckner, 2022). Since the correlation coefficient is positive, this lets the researcher know that
as the value of one variable increases, the value of the other variable will also tend to increase.
(b) What is r2 for the Pearson correlation? What does it mean?
R2 is a common measure of goodness of fit and is also a statistical measurement that can
tell how well the regression line approximates the actual data (Piepho, 2023). In output 8.2, the
r2 for the Pearson correlation indicates that approximately 10% of the variance in math
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achievement test scores can be predicted by mother’s education which informs the researcher
about the fit of the model (Morgan, Barrett, Leech & Gloeckner, 2022)
(c) Compare the Pearson and Spearman correlations on both correlation size and significance
level.
The Pearson correlation is best utilized when evaluating the relationship between two
continuous variables whereas the Spearman correlation is best utilized on ranked values for the
variables (Morgan, Barrett, Leech & Gloeckner, 2022). In output 8.2, the Pearson correlation is .
338 and the Spearman’s correlation is .315 reflecting that the two correlations are relatively
close.
(d) When should you use which type in this case?
The Pearson correlation should be utilized when the researcher has two variables that are
normal/scale, and the Spearman correlation should be used when one or both of the variables are
ordinal or in the case, one or both of the variables are not normally distributed (Morgan, Barrett,
Leech & Gloeckner, 2022). Determining the appropriate selection will allow for the data to be
more clearly interpreted.
D6.8.5 In Output 8.5, what do the standardized regression weights or coefficients tell you
about the ability of the predictors to predict the dependent variable?
The standardized regression weights or coefficients tell the researcher one primary fact
about the ability of the predictors to predict the dependent variable. Essentially, when all
variables are used as predictors, the standardized coefficients allow the researcher to compare the
amount that each variable contributes to predicting outcomes and standardized predictors put
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them all on the same scale (Morgan, Barrett, Leech & Gloeckner, 2022). In output 8.5, this can
be seen in the data for math achievement. Once all of the data has been put on the same scale, it
is much easier to identify the predictors that most strongly predict the dependent variable.
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References
Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for
introductory statistics: Use and interpretation, sixth edition (6th ed.). Routledge.
Piepho, H. (2023). An adjusted coefficient of determination (R 2 ) for generalized linear mixed
models in one go. Biometrical Journal, 65(7), e2200290-
e2200290. https://doi.org/10.1002/bimj.202200290
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