Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337794503
Author: PECK
Publisher: Cengage
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Textbook Question
Chapter 5.3, Problem 45E
The first Batman movie was made over 50 years ago in 1966. Over the years, Batman has been played on screen by a number of actors and even by a Lego figure in the Lego Batman movies. In the original comic books, Batman was 188 centimeters tall (about 6′2″) and weighed 95 kilograms (about 210 pounds). The article “50 Years of Batman on Film: How Has His Physique Changed?” (economist.com, March 28, 2016, retrieved April 22, 2017) included the heights and weights of all the onscreen Batmen in the table below.
With x = Height and y = Weight, the equation of the least-squares line is
- a. Calculate the residuals.
- b. Construct a residual plot. Are there any unusual features of the residual plot?
- c. The observation for Lego Batman (4, 4) is far removed from the other values in the data set (not surprising!). Is this observation influential in determining either the slope of the least-squares line, or the intercept, or both? Justify your answer.
Expert Solution & Answer
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1. Find the mean of the x-values (x-bar)
and the mean of the y-values (y-bar) and write/label each here:
2. Label the second row in the table using proper notation; then, complete the table. In the fifth and sixth
columns, show the 'products' of what you're multiplying, as well as the answers.
X
y
x minus x-bar y minus y-bar (x minus x-bar)(y minus y-bar)
(x minus x-bar)^2
xy
16
20
34
4-2
5 2
3. Write the sums that represents Sxx and Sxy in the table, at the bottom of their respective columns.
4. Find the slope of the Regression line: bi
=
(simplify your answer)
5. Find the y-intercept of the Regression line, and then write the equation of the Regression line.
Show your work. Then, BOX your final answer. Express your line as "y-hat equals...
Apply STATA commands & submit the output for each question only when
indicated below
i.
Generate the log of birthweight and family income of children. Name
these new variables Ibwght & Ifaminc. Include the output of this
code.
ii. Apply the command sum with the detail option to the variable
faminc. Note: you should find the 25th percentile value, the 50th
percentile and the 75th percentile value of faminc from the output -
you will need it to answer the next question Include the output of this
code.
iii.
iv.
Use the output from part ii of this question to Generate a variable
called "high_faminc" that takes a value 1 if faminc is less than or
equal to the 25th percentile, it takes the value 2 if faminc is greater
than 25th percentile but less than or equal to the 50th percentile, it
takes the value 3 if faminc is greater than 50th percentile but less than
or equal to the 75th percentile, it takes the value 4 if faminc is greater
than the 75th percentile. Include the outcome of this code…
solve this on paper
Chapter 5 Solutions
Introduction To Statistics And Data Analysis
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