1. A researcher was interested in investigating the impact of Food and Drink in a
Computer Classroom. The amount of food and drink consumed was correlated with
alertness in class. The researcher also wanted to control for the variable of interest in
subject matter when examining this relationship.
Researcher A wanted to use bivariate correlations to examine this problem. S/he divided
the sample into two groups that indicated different levels of interest (those taking the
course as a requirement and those taking as an elective) and ran a bivariate correlation for
Researcher B used partial correlation to examine this issue. S/he used an interest scale
(scaled 1 to 5) to measure interest in the subject matter and used this score as a control
variable before examining the relationship food/drink consumed and alertness.
Which researcher is addressing the problem most appropriately. In your response, provide
at least two convincing reasons for your selection indicating why this approach is better
than the other one.
2. Examine the following Venn diagram carefully.
2a. Which proportion of this diagram represents the partial correlation
between X1 and Y, controlling for the influence of X2?
A. (B+D) divided by (A+B+C+D)
B. (B+C) divided by (A+B+C+D)
C. C divided by (A+C)
D. B divided by (A+B)
2b. Which part(s) of this diagram represent(s) the portion of the dependent
variable explained by semi-partial correlation with X2, controlling for the
influence of X1?
B. B & D
D. C & D
2c. Which part(s) of the diagram represent(s) represent the overall R2 using
both X1 and X2 to predict Y?
E F G
3. Examine the following results from a multiple regression analysis. There are three
predictor variables that have been used to predict alertness in this class.
X1 - Amount of
Caffeine (prior to
class, of course)
X2 - Amount of
time spent talking
sports or political
X3 - Hours of
sleep the night
B .325 3.24 4.2
95% C.I. of B .013 to .525 1.5 to 4.97 -2.22 to 6.32
t test (Sig.) .467 (.823) 3.50 (.003) 2.74 (.032)
Beta .114 .800 .695
Zero-order Correlation .225 .562 .499
Partial .022 .332 .233
Semi-Partial .011 .257 .125
VIF 2.50 2.75 8.90
Tolerance .825 .752 .325
Constant (Intercept) = 7.25
a. Select the best predictor and indicate at least three reasons for this selection.
b. Identify the variable that appears to exhibit the most multicollinearity and indicate at
least two reasons why.
c. Write the regression equation that would be used to predict alertness, based on the
three predictor variables above.
4. Describe a situation in which Analysis of Covariance (ANCOVA) would be used
in your area of specialization.
a, Describe the DV and how it will be measured.
b. Describe the covariate(s) and why it(they) is(are) appropriate.
c. Describe the conditions of the IV (treatment variable) and why this variable
would impact the DV after accounting for the covariate(s).
d. Describe what evidence will allow you to conclude that the IV had an impact
on the DV, after controlling for the covariate(s).
e. Explain how regression is used to adjust the group means prior to conducting a
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Researcher B is addressing the problem most appropriately because of the following reasons:
1. We know that the partial correlation is being used to find the relationship between the variables by controlling the effect of one or more variables. Whereas, bivariate correlation defined the relationship between the variables only but it does not control the other variable(s). Since, researcher B is using partial correlation to examine this issue and as an interest scale (scaled 1 to 5) to measure interest in the subject matter and used this score as a control variable before examining the relationship food/drink consumed and alertness, therefore, we can say that researcher B’s approach is better than the researcher A.
2. Researcher A divided the sample into two groups that indicated different levels of interest (those taking the course as a requirement and those taking as an elective) and ran a bivariate correlation for each group....