STATS Quiz 4 Questions

Question 1
The following output is based on data from the foam
height investigation of Quiz 2. Use the information in this output to answer Questions
1 to 6.
Two-way ANOVA: foam ht versus
glass temp, angle

Source DF SS MS F P
glass
temp 1 40.11 40.11 0.38 0.541
angle 2 2310.89 1155.44 11.00 0.000
Interaction 2 37.56 18.78 0.18 0.837
Error 30 3151.67 105.06
Total 35 5540.22
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(Bartlett’s
Test: Test Statistic = 2.21, p-value = 0.820)
(Levene’s
Test: Test Statistic = 1.21. p-value = 0.328)

What does
the p-value of0.837tell us about interaction?
Answer

There
is very strong evidence of interaction.

There is no/insufficient interaction.

There
is some evidence of interaction.

There
is no evidence that average foam height differs for different glass
temperature (allowing for the effect of pouring angle)

We reject the null
hypothesis if p-value is small (smaller than significance level). The p-value
0.837 tells us that we can’t reject the null hypothesis for the interaction. As
the null hypothesis is interaction = 0 so p-value =0.837 gives the selected
interpretation.
Question 2

What would interaction mean in the context of this
analysis
Answer

Interaction means that the effect of
pouring angle differs for different glass temperatures.

Interaction
means that the effect of foam height differs for different glass
temperatures.

Interaction
means that the effect of pouring angle differs for different foam
heights.

Interaction
means that when people drink together they engage in conversation.

The
variables of consideration are angle and glass temperature and interaction term
means the relation between them thus the answer.
Question 3

The p-value of0.541tells us that…
Answer

There
is very strong evidence that average foam height differs for different glass
temperatures (allowing for the effect of pouring angle).

There
is some evidence that average foam height differs for different glass temperatures
(allowing for the effect of pouring angle).

There
is no evidence that average foam height differs for different pouring angle
(allowing for the effect of glass temperatures)

There is no evidence that
average foam height differs for different glass temperatures (allowing for
the effect of pouring angle)

As
p value is larger so we fail to reject the null hypothesis of insignificance
and thus there is no significance for the considered variable which is glass
temperature.
Question 4

The p-value of0.000tells us that …
Answer

There is extremely strong
evidence that average foam height differs for different pouring angles
(allowing for the effect of glass temperature).

There
is some evidence that average foam height differs for different pouring
angles (allowing for the effect of glass temperature).

There
is insufficient evidence that average foam height differs for different
glass temperature (allowing for the effect of pouring angles).

There
is extremely strong evidence that average foam height differs for
different glass temperature (allowing for the effect of pouring
angles).

P-value
is 0 suggesting rejection of null hypothesis i.e. the considered variable is
significant and the considered variables for whose p-value we are considering
is angle so the answer.
Question 5

Which comment is correct for the first plot.
Answer

The
assumption of equal variance (for all combinations on the factor categories)
is not reasonable.

The assumption of equal
variance (for all combinations on the factor categories) is reasonable.

The
plot is reasonably straight, so the assumption that foam heights are normally
distributed about their location mean (or within each combination of
categories) is reasonable.

The
plot is curved, so the assumption that foam heights are normally distributed
about their location mean (or within each combination of categories) is not
reasonable.

As
each confidence interval is overlapped hence the answer.
Question 6

Which comment is correct about the second plot?
Answer

The
assumption of equal variance (for all combinations of the factor categories)
is not reasonable.

The
assumption of equal variance (for all combinations of the factor categories)
is reasonable.

The plot is reasonably
straight, so the assumption that foam heights are normally distributed about
their local means (or within each combination of categories) is reasonable.

The
plot is curved, so the assumption that foam heights are normally distributed
about their local means (or within each combination of categories) is not
reasonable.

As
it’s the Normal probability plot and the dots are almost on the lines hence the
answer.
Question 7

Data was gathered on spatial perception by asking their subjects to
estimate either or both of a 5cm length and a 10cm length. They also recorded
the subject’s gender, age range (in decades: 10–19, 20–29, 30–39, 40–49) and
whether they were right-handed or left-handed. The following analyses are based
on this data set.

The following output relates to the estimates for the 10cm length. Use
the information in this output to answer Questions 7 to 11.

General Linear Model: Estimate of versus
Left/Right H, Age_group_10

Analysis of Variance for Estimate of Length(cm)_10,
using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj
MS F P
Left/Right
Handed_10 1 0.862 0.155 0.155 0.02 0.887
Age_group_10 3 6.962 34.895 11.632 1.53 0.217
Left/Right
Handed_10*Age_group_10 3 85.213 85.213 28.404 3.73 0.016
Error 57 434.326 434.326 7.620
Total 64 527.362

S = 2.76039 R-Sq = 17.64% R-Sq(adj) =
7.53%
What does the p-value of 0.887 tell us?
Answer

There
is strong evidence of interaction (i.e. that the differences between average
lengths) estimated by the various age groups are different for right and left
handed people).

There
is no evidence of any difference in average length estimated by different age
groups, averaged over handedness.

There is no evidence of any difference in
average length estimated by left and right handed people, averaged over age
groups.

There
is strong evidence of a linear relationship between age and estimated length.

By
using the same logic as before.
Question 8

What does the p-value of 0.217 tell us?
Answer

There
is strong evidence of interaction (i.e. that the differences between average
lengths) estimated by the various age groups are different for right and left
handed people).

There is no evidence of any
difference in average length estimated by different age groups, averaged over
handedness.

There
is no evidence of any difference in average length estimated by left and
right handed people, averaged over age groups.

There
is strong evidence of a linear relationship between age and estimated length.

1.5
points
Question 9

What does the p-value of 0.016 tell us?
Answer

There is strong evidence of
interaction (i.e. that the differences between average lengths) estimated by
the various age groups are different for right and left handed people).

There
is no evidence of any difference in average length estimated by different age
groups, averaged over handedness.

There
is no evidence of any difference in average length estimated by left and
right handed people, averaged over age groups.

There
is strong evidence of a linear relationship between age and estimated length.

1.5
points
Question 10

What does the value of R-sq(adj) tell us?
Answer

Only
7.5% of the variation in estimated lengths has been explained by fitting this
model.

Only
17.6% of the variation in estimated lengths has been explained by fitting
this model.

Only 7.5% of the variation
in estimated lengths has been explained by fitting this model, adjusted for
the number of terms in the model.

Only
17.6% of the variation in estimated lengths has been explained by fitting
this model, adjusted for the number of terms in the model.

1.5
points
Question 11

What is the following plot telling us?
Answer

There
is no interaction.

The
effects are acting additively.

Left
handed people tend to estimate greater lengths than right handed people for
the 10-19, 30-39 and 40-49 year age group, but strongly the other way around
for the 20-29 year age group.

Right
handed people tend to estimate greater lengths than left handed people for
the 10-19, 30-39 and 40-49 year age group, but strongly the other way around
for the 20-29 year age group.

1.5
points
Question 12

The following output was obtained from an analysis comparing estimates
for 5cm across age groups and genders. What does the output tell us?

Tukey 95.0% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of
Age_group_5

Age_group_5 = 10-19 subtracted from:
Age_group_5 Lower Center Upper —–+———+———+———+-
20-29 0.232 3.539 6.846 (——*——)
30-39 -2.525 2.911 8.347 (———-*———-)
40-49 -2.599 1.446 5.492 (——-*——-)
—–+———+———+———+-
-5.0 0.0 5.0 10.0

Age_group_5 = 20-29 subtracted from:
Age_group_5 Lower Center Upper —–+———+———+———+-
30-39 -6.160 -0.628 4.903 (———-*———-)
40-49 -6.266 -2.093 2.081 (——–*——-)
—–+———+———+———+-
-5.0 0.0 5.0 10.0

Age_group_5 = 30-39 subtracted from:
Age_group_5 Lower Center Upper —–+———+———+———+-
40-49 -7.467 -1.464 4.538 (———–*———–)
—–+———+———+———+-
-5.0 0.0 5.0 10.0

Answer

The only age groups with
clear evidence of a difference in average estimates for the 5cm length were
the 10-19 and 20-29 age groups.

The
only age groups without clear evidence of a difference in average estimates
for the 5cm length were the 10-19 and 20-29 age groups.

There
is strong evidence of a difference in average estimates for all of the age
groups.

There
is no evidence of a difference in average estimates for any of the age
groups.

2 points

Question 13

A study of rental prices for houses considered the effects of distance
from public transport (km2tpt), number of bedrooms (b-rms) and
letting agent (agentA). In the area being studied, the two largest
letting agents accounted for the majority of rentals, so the analysis was
initially restricted to these two agents only. Note that the variableagentAtakes the values 1 for houses let through agent A and 0 for those let
through agent B.

The data obtained from this study were entered into Minitab, and the
following printout was obtained as part of the analysis. Use the information in
this printout to answer Questions 13 to 19.
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1.
Regression Analysis: rent$ versus b-rms, km2tpt,
agentA

The regression equation is
rent$ = 165 + 55.0 b-rms – 33.9 km2tpt + 5.23
agentA

Predictor Coef SE Coef T P
Constant 164.999 6.195 26.64 0.000
b-rms 54.967 1.832 30.00 0.000
km2tpt -33.926 2.899 -11.70 0.000
agentA 5.234 3.583 1.46 0.148

S = 14.6181 R-Sq = 94.3% R-Sq(adj) =
94.1%

Analysis of Variance
Source DF SS MS F P
Regression 3 259042 86347 404.08 0.000
Residual Error 73 15599 214
Total 76 274641

Unusual Observations
Obs b-rms rent$ Fit SE
Fit Residual St Resid
19 3.00 245.00 277.32 3.14 -32.32 -2.26R
25 3.00 281.00 310.90 2.80 -29.90 -2.08R
60 3.00 265.00 294.08 2.29 -29.08 -2.01R
R denotes an observation with a
large standardized residual
The p-value of 0.000 for b-rms indicates that …
Answer

There is extremely strong
evidence that the number of bedrooms affects the average rental price in a
linear fashion, after allowing for the other predictors.

There
is extremely strong evidence that distance to transport affects the average
rental price in a linear fashion, after allowing for the other predictors.

There
is no evidence that letting agent affects the average rental price in a
linear fashion, after allowing for the other predictors.

The
model fits the data well.

1.5
points
Question 14

The p-value of 0.000 for km2tpt indicates that …
Answer

There
is extremely strong evidence that the number of bedrooms affects the average
rental price in a linear fashion, after allowing for the other predictors.

There is extremely strong
evidence that distance to transport affects the average rental price in a
linear fashion, after allowing for the other predictors.

There
is no evidence that letting agent affects the average rental price in a
linear fashion, after allowing for the other predictors.

The
model fits the data well.

1.5
points
Question 15

The p-value of 0.148 indicates that …
Answer

There
is extremely strong evidence that the number of bedrooms affects the average
rental price in a linear fashion, after allowing for the other predictors.

There
is extremely strong evidence that distance to transport affects the average
rental price in a linear fashion, after allowing for the other predictors.

There is no evidence that
letting agent affects the average rental price in a linear fashion, after
allowing for the other predictors.

The
model fits the data well.

Question 16

Which of the following statements is correct
regarding the below plots?
.jpg”>
Answer

The
assumption that rental prices are normally distributed about the average for
the relevant predictor values appears to be reasonable.

There
is no indication of a non-linear trend for rental prices against distance to
transport, and the variance appears to be fairly consistent. The variance
appears very different for the two agents.

There
is an indication of a quadratic trend for rental prices against distance to
transport, and the variance appears to be fairly consistent. The variance
appears fairly consistent for the two agents.

There is no indication of a
non-linear trend for rental prices against distance to transport, and the
variance appears to be fairly consistent. The variance appears fairly
consistent for the two agents.

Question 17

Which of these comments is correct regarding
the plot below?
.png”>

Answer

The assumption that rental prices are normally
distributed about the average for the relevant predictor values appears to be
reasonable.

There is no indication of a non-linear
trend for rental prices against distance to transport, and the variance
appears to be fairly consistent. The variance appears very different for the
two agents.

There is an indication of a quadratic
trend for rental prices against distance to transport, and the variance
appears to be fairly consistent. The variance appears fairly consistent for
the two agents.

There is no indication of a non-linear
trend for rental prices against distance to transport, and the variance
appears to be fairly consistent. The variance appears fairly consistent for
the two agents.

1 points
Question 18

Approximately
how many observations would you expect to be reported with anRbeside
them in the Minitab output for this analysis?
Answer

3

4

5

6

0.5 points
Question 19

Are
any serious concerns raised by the “Unusual Observations” reported in the
output above? Select the most appropriate answer.
Answer

Yes, we don’t want any unusual
observations.

Yes, we only want one unusual observation
per data set.

Not really – there are less than the expected number
calculated above.

Not really – there are more than the
expected number calculated above.