W#2 BENCH Linear Regression & Correlation -- Version A
After an extended closure for a public health emergency, the management
at Metro Arena is reviewing its hospitality for roving ushers, bathroom
attendants and other greeters not specifically assigned to monitor seating
areas, in anticipation of its reopening. They wondered about the association
between the number of these seemingly surplus staffers on duty at an event
and the number of past complaints or concerns brought to their attention at
the main customer service counter. Some randomly selected data is as
follows, where the variable x
represents the number of these staffers at
selected events, and the variable y
represents the number of complaints or
concerns filed during that event.
COMMENTS & HINTS:
Use computer and/or calculator technology to your
advantage so to minimize tedious calculations! Round as requested, when
necessary.
x
37
40
25
45
28
y
24
20
32
16
28
What are the values that form the centroid for this bivariate data: x
, y
?
Report the value of x
, here, without insignificant digits or extra
characters: [A]
Report the value of y
here, without insignificant digits or extra
characters: [B]
-
A = 35 -
B = 24 Create a scatter plot of this bivariate data. What is the apparent trend?
-
The trend is negative. As the number of staffers at the arena for an
event decreases, the number of complaints increases
correspondingly.
What is the value of the Pearson product moment correlation
coefficient, r
? Express the answer with sign in decimal form, rounded to the
nearest thousandth
-
-0.986
How best or most accurately can the association or correlation evidenced in
the data be described?
-
The association or correlation is high, very strong and negative.
What is the equation of the trend or regression line that best represents this
data? Express the values in decimal form, rounding the slope and y-intercept
to the nearest hundredths when reporting the answers.
Report the slope here, rounded as requested, including its sign to indicate
positive or negative trend: [A]
Report the y
-intercept here, rounded as requested, including its sign: [B]
-
A = -0.75
-
B = 32 ?
What is the value of the coefficient of determination, r
2
? -
0.973
What percentage of the variability evidenced between the independent
(input) and dependent (output) variables is attributable to the linear
regression model? Express the answer rounded to the nearest whole
percent with percent symbol. -
97%
What percentage of the variability evidenced between the independent
(input) and dependent (output) variables is not
attributable to the linear
regression model?
-
3%
If 42 staffers are on duty, predict the number of complaints, according to the
model.
Express the answer rounded to the nearest whole complaint. -
19
