Statistic 216 Assignment
Please do this Statistic assignment.
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0/19 Questions Answered
Assignment 5
Q1 Social Warmth
15 Points
Social warmth is a term referring to the feeling of being connected
to others. A study conducted in 2016 looked at a potential
relationship between physical warmth (body temperature) and
social warmth among a group of 54 volunteers. These volunteers
had their oral temperature taken by a registered nurse and then
assessed themselves using a scale of 1 to 5 on twelve items related
to feeling of social connection for which the average was recorded.
Higher average scored indicated higher levels of social warmth.
The theory was that thermoregulatory system, which helps maintain
a relatively warm internal body temperature, may also help people
assess feelings of social connection.
Q1.1 Explanatory and Response
2 Points
Match the two variables collected with their role in this study. Type
A for the response variable and B for the explanatory variable.
Body temperature (in degrees Celsius)
Enter your answer here
Social warmth average score (scale of 0 to 5)
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Enter your answer here
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Q1.2 Type of study
1 Point
Is this an observational study or a randomized experiment?
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Q1.3 Scatterplot – form
1 Point
Among the 54 participnts, the mean body temperature was
with a standard deviation of while the mean
social warmth average score was with a standard deviation
of . Below is a scatterplot of the data.
Observational study, because these are volunteers, not a
random sample.
!
Randomized experiment, because the researchers are
investigating a relationship between two variables.
!
Observational study, because the volunteers self-reported their
feelings of social warmth.
!
Observational study, because body temperature was not
randomly assigned.
!
36.72 C 0.30 C
4.163
0.405
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What form is the relationship?
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Q1.4 Scatterplot – direction
1 Point
What is the direction of this relationship?
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Q1.5 Scatterplot – unusual observations
1 Point
Linear!
Non-linear!
Positive!
Negative!
Direction is not clear!
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1 Point
There is one observation which could be argued
appears to be far from the rest of the data. Would you anticipate
this point being influential?
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Q1.6 Scatterplot – strength
1 Point
Which of the following is the correlation coefficient for these data?
You should be able to answer this question without using R !
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Q1.7 Least Squares Regression
2 Points
(37.2 C, 3.3)
Yes, because the social warmth score of is far below the
average social warmth score.
! 3.3
No, because the body temperature of is near the average
body temperature.
! 37.2
Yes, because the body temperature of is far from the
average body temperature.
! 37.2
No, because the social warmth score of is near the average
social warmth score.
! 3.3
! r = 0.213
! r = 0.721
! r = 0.032
! r = 0.348
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The lm() function in R provides the following output. Use this
information to determine the values of and for these data.
Report your answers to four decimal places
:
Enter your answer here
:
Enter your answer here
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Q1.8 Slope
1 Point
Select the most appropriate interpretation of the slope of the
regression line.
b0 b1
b0
b1
A 1 unit increase in social warmth score average is associated
with a 0.4612 degree Celsius increase in body temperature.
!
A 1 unit increase in social warmth score average is associated
with a 12.77 degree Celsius decrease in body temperature.
!
The predicted social warmth score average decreases by 12.77
for each 1 degree Celsius increase in body temperature.
!
The predicted social warmth score average increases by 0.4612!
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Q1.9 Predicted values and Residuals
1 Point
One of the fifty-four volunteers had an average social warmth score
of and a body temperature of . Calculate the residual
for this person. Round your answer to three decimal places. Hint:
first calculate the volunteer’s predicted social warmth!
Enter your answer here
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Q1.10 Coefficient of determination
1 Point
From R , it was found that and .
Calculate the coefficient of determination. Convert your answer to
a percentage, then round to one decimal place. Type in your
calculated answer below. Write the value only; do not include the %
sign.
Enter your answer here
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Q1.11 Notation for previous
The predicted social warmth score average increases by 0.4612
for each 1 degree Celsius increase in body temperature.
!
4.4 36.6 C
SST = 8.71 SSE = 7.65
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1 Point
What notation should be used to represent the value you calculated
in the previous problem?
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Q1.12 Interpret coefficient of determination
1 Point
Let ‘X’ % represent your calculated coefficient of determination.
Select the best interpretation of X, in the context of the problem.
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Q1.13 Causation
1 Point
Suppose a test of association provides strong evidence of a
! R2
! r
! b0
! b1
The probability of seeing this sample slope, or something further
from 0, is X %.
!
The strength and direction of the linear relationship between
body temperature and average social warmth score is X %.
!
X % of the variation in social warmth average score can be
explained by changes in body temperature.
!
X % of the variation in body temperature can be explained by
changes in social warmth average score.
!
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Suppose a test of association provides strong evidence of a
relationship between body temperature and social warmth. Can
the researchers conclude that increasing body temperature causes
increased feelings of social connected-ness?
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Q2 True/False 1
1 Point
If the correlation coefficient between variables and is positive,
then we can say that and have a positive linear relationship.
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Q3 True/False 2
1 Point
If the correlation coefficient between variables and is positive,
then the slope of the least squares regression line using to
predict will also be positive.
Yes, because the slope is positive.!
No, because body temperature was not randomly assigned.!
No, because social warmth average score was not randomly
assigned.
!
No, because the sample is made up of volunteers.!
x y
x y
True!
False!
x y
x
y
True!
False!
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Q4 True/False 3
1 Point
The correlation coefficient between and must have the same
value as the slope between and .
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Q5 MarioKart
4 Points
Data were collected on 143 eBay sales of Mario Kart for Nintendo
Wii. The variables collected include:
duration: auction length, in days
n_bids: number of bids
cond: game condition (new or used)
start_pr: starting price of the auction ($)
total_pr: total price = auction price + shipping price ($)
ship_inc: whether shipping was included (ship_pr = 0) or not
ship_sp: shipping speed
seller_rate: seller’s rating on eBay
stock_photo: whether the auction feature photo was a stock
photo or not
wheels: number of Wii wheels (specialized controllers for the
game) included
x y
x y
True!
False!
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Q5.1 Observational units
1 Point
Identify the observational units.
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Q5.2 Variables
2 Points
Below is a scatterplot displaying some of the variables collected.
Select all the variables which are displayed.
Video games!
eBay sellers!
eBay sales of Mario Kart for Nintendo Wii!
eBay buyers!
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Q5.3 Interactions
1 Point
Among which types of sales does it appear that whether shipping is
included and the number of bids interact to explain total price?
Select all that apply.
duration: auction length, in days
n_bids: number of bids
cond: game condition (new or used)
start_pr: starting price of the auction
total_pr: total price
ship_inc: whether shipping was included (ship_pr = 0) or not
ship_sp: shipping speed
seller_rate: seller’s rating on eBay
stock_photo: whether the auction feature photo was a stock
photo or not
wheels: number of Wii wheels (specialized controllers for
the game) included
Sales with 0 wheels included
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Sales with 1 wheel included
Sales with 2 wheels included
