# PSY 570 -- Homework Assignment #1

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```					                                            PSY 570 -- Homework Assignment #1
Correlation and Multiple Regression
Total points: 30

For this and all homework assignments, use the Aerobic Fitness Data set. For this and all homework assignments, you are
to hand in two portions: (1) your answers/interpretations/conclusions to the problems and (2) the EcStatic printouts for the
problems. Write your answers/interpretations on separate paper. Do not write them on this sheet or on the printouts. Be
sure your answers are legible and that your pages and printouts are neatly organized and stapled together.

One of the researchers is interested in determining the proportion of variability in final fitness level (AEROBIC2) that
is accounted for by initial fitness level, plans to continue exercise, and rated level of enjoyment, in that order. Conduct
the necessary analyses to complete each of the following problems (the level of significance is set at .05 for all
analyses):

a. Based on comparisons of the means and medians, do any of the quantitative variables show evidence of being
severely skewed? Justify your answer (and show your calculations of the difference between mean and median in
terms of standard errors).

b. Use EcStatic to construct scatterplots for the dependent variable (AEROBIC2) against each of the quantitative
predictor variables (i.e., For each scatterplot, put the DV on the vertical axis, and the predictor variable on the
horizontal axis). Do either of the relationships appear to be nonlinear? Justify your answer.

c. Construct an APA-style correlation matrix showing the intercorrelations and summary statistics for the variables of
interest to the researcher. Remember that the DV is listed first in the table, followed by the predictor variables in
their order of interest (or their order of entry into the regression equation). Label the correlation table as Table 1.
Do not forget to indicate which correlations are significant and to include an appropriate Table title and Table
notes.

d. After getting the full model (final step), calculate sr2 for each predictor in the full model. Show your calculations
(and include your printouts) for each sr2.

e. For the full model (final step), interpret the meaning of each regression coefficient in plain English (Remember this
means that, because you have three predictors, you=ll have three separate interpretations: one for each slope value).

f.   Construct an APA-style multiple regression table (you may also do a worksheet showing each of the 3 steps if you
wish, but whether you choose to do a worksheet or not you must turn in your regression printouts showing each
step where a predictor was added). In the table, show the values of B, SE B,I and sr2 for each of the predictors in
the final model the values of intercept, R2 , adj. R2, R. Be sure to indicate which values of B and are significant
and if the R is significant. Label it Table 2. Do not forget to give the table an appropriate title and to include the
appropriate Table notes.

g. Write an APA-style Results section for the overall analyses (correlation and regression) in which you include at
least each of the following in your discussion. Write it as a Results section, not as a list of answers to the questions
and remember to refer the reader to the information contained in your Tables 1 and 2 as appropriate:

\$   Statements in plain English of the pattern of correlation between the DV and each of the predictors.
\$   The regression equation for the full model in the form:
AEROBIC2' = a + b1AEROBIC0 + b2 CONTINUE + b3FUNLEVEL (where you supply the calculated values
for the intercept and slope coefficients)
\$   Identification of the total proportion of variability in final fitness level that is accounted for by the full
regression model and a statement of whether or not that overall proportion is significantly different from 0,
along with a justification for that statement (which includes the minimum necessary identifying statistical
information reported in appropriate format).
\$   Statement of whether or not each of the predictors in the final model accounts for a significant, unique
proportion of variability in final fitness level along with justification for your statements (which includes the
minimum necessary identifying statistical information reported in appropriate format) and how much unique
variance each accounts for.

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