Question

Body frame size is determined by a person's wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals. The data is displayed below. 5 5.5 6 6.5 7 7.5 8 8.5 9 60 65 70 75 80 Wrist Circumference (in) Height (in) Coefficients: Estimate Std Err t-value p-value (Intercept) 33.5375 4.4833 7.4806 4.78 E -8 wrist 5.1405 0.6361 8.0818 1.11 E -8 Residual standard error: 2.9252 on 27 degrees of freedom R-squared: 0.7075, Adjusted R-squared: 0.6967 F-statistic: 65.3151 on 1 and 27 DF, p-value: 1.11 E -8 a) Write the equation of the best-fit line. Use x and y for your variables. b) Calculate the correlation coefficient. c) Identify the coefficient of determination. d) Use the equation of the best-fit line to predict the height of a person with a wrist circumference of 6 inches. inches e) One of the points on the scatterplot is (7,74.3). Calculate the residual for this point. inches f) The mean wrist circumference for this data is 6.997 inches. Calculate the mean height for this data. inches g) When predicting heights, what is a "typical" error using this linear model? inches h) What fraction of variability in heights can be explained using the linear model of height vs wrist circumference? Enter your response as a decimal. i) Calculate the correlation coefficient if the heights are measured in feet. (All heights divided by 12.)

Answer #1

Body frame size is determined by a person's wrist circumference
in relation to height. A researcher measures the wrist
circumference and height of a random sample of individuals. The
data is displayed below.
55.566.577.588.595560657075808590Wrist Circumference (in)Height
(in)
Coefficients:
Estimate
Std Err
t-value
p-value
(Intercept)
29.7403
5.1272
5.8004
1.74 E -6
wrist
6.0758
0.7135
8.5154
7.70 E -10
Residual standard error: 4.101 on 33
degrees of freedom
R-squared: 0.6872, Adjusted
R-squared: 0.6778
F-statistic: 72.512 on 1 and 33 DF,
p-value: 7.70...

1. The table lists height (in) and weights (lb) of randomly
selected 8 students.
Height (in) 60 65 66 68 60 67 69 70
Weight (lb) 150 152 156 160 160 167 168 170
(a) Find the the value of coefficient of correlation r.
(b) Find the equation of the line of best best fit (trend line).
What does variable y represents?
(c) Estimate weight of a student from the same group who is 64
inches tall.

A pediatrician wants to determine the relation that may exist
between a child's height and head circumference. She randomly
selects 5 children and measures their height and head
circumference. The data are summarized below. Complete parts (a)
through (f) below. Height (inches), x 26.75 25.5 27.75 26.5 27.5
Head Circumference (inches), y 17.3 17.1 17.6 17.3 17.5 a)
Treating height as the explanatory? variable, x, use technology to
determine the estimates of ?0 and ?1. (b) Use technology to compute...

Height (inches) x: 27 25 27.75 26.75 26.5
Head Circumference (inches) y: 17.5 16.9 17.6 17.3 17.3
A pediatrician wants to determine the relation that may exist
between a child's height and head circumference. She randomly
selects 5 children and measures their height and head
circumference. The data are summarized below. Complete parts (a)
through (f) below.
a) Treating height as the explanatory variable, x, use
technology to determine the estimates of beta 0β0 and beta 1β1.
beta 0β0almost equals≈b...

Use the classroom dataset. A researcher wants to be able to use
shoe size to predict height.
Shoe size= 6, 9, 7.5, 9.5, 8, 10.5, 8, 8, 7.5, 7.5, 9, 9, 8.5,
11.5, 8.5, 9, 7, 5, 8, 8, 8.5, 6.5, 6
Height(in)= 62, 67, 62, 69, 63, 67, 66, 63, 68, 64, 63, 66, 65,
72, 64, 65, 66, 61, 67, 64, 65, 60, 64
A) what variable is the response variable and which is the
predictor variable?
B)...

A researcher did a study to investigate the potential
relationship between diastolic blood pressure (DBP, dependent
variable) and age (independent variable) for boys 5 to 13 years
old. The data were analyzed using a simple linear regression model
and the statistical results were as following.
Estimate Std. Error t value Pr(>|t|)
b0 (Intercept) 49.8844 5.7272 8.710 1.12e-05
b1 for Age 2.1927 0.6025 3.639 \ 0.00541
Residual standard error: 5.552 on 9 degrees of freedom
Multiple R-squared: 0.5954, Adjusted R-squared: 0.5505...

The cost of a leading liquid laundry detergent in different
sizes is given below.
Size (ounces)
Cost ($)
16
3.79
32
4.79
64
5.59
200
10.49
Part (a)
Using "size" as the independent variable and "cost" as the
dependent variable, draw a scatter plot.
Part (b)
Does it appear from inspection that there is a relationship between
the variables? Why or why not?
Yes, it appears that cost increases with size.No, there is no
visible relationship between the variables. ...

Researchers measured oxygen consumption in 10 seals. They
measured oxygen consumption for each seal under two conditions: (1)
when they did a dive for food (referred to as a feeding dive) and
(2) when they did a dive that was not food-related (referred to as
nonfeeding dives). They wanted to learn about the
relationship between oxygen consumption for feeding dives and
oxygen consumption for nonfeeding dives so they fit a linear
regression model with Y = Oxygen consumption in feeding...

Match the statistics term with its BEST
definition.
Question 2 options:
A key requirement for using correlation and regression models is
to collect this type of data.
With bivariate data, the result of MINIMIZING the sum of squared
distances between the observed and predicted values (residuals) for
a linear model.
This quantity is computed by subtracting the observed response
variable from the predicted response variable.
With bivariate data, when one variable increases a second
variable decrease implies this relationship.
A...

The following are advertised sale prices of color televisions at
an electronics store.
Size (inches)
Sale Price ($)
9
137
20
187
27
277
31
447
35
1177
40
2177
60
2497
A. Decide which variable should be the independent variable and
which should be the dependent variable.
Independent variable: size; Dependent variable: OR sale price
Independent variable: sale price; Dependent variable:
size
B. Draw a scatter plot of the data.
C.
Does it appear from inspection that there is...

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