Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
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Chapter 14, Problem 71CR
a.
To determine
Construct a curve for the given equation.
b.
To determine
Check whether the given statement is reasonable or not.
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The relationship between yield of maize (a type of corn), date of planting, and planting density was investigated in an article. Let the variables be defined as follows.
y = maize yield (percent)
x1 = planting date (days after April 20)
x2 = planting density (10,000 plants/ha)
The following regression model with both quadratic terms where
x3 = x12
and
x4 = x22
provides a good description of the relationship between y and the independent variables.
y = ? + ?1 x1 + ?2 x2 + ?3 x3 + ?4 x4 + e
(a)
If ? = 21.05, ?1 = 0.652, ?2 = 0.0025,
?3 = −0.0204,
and
?4 = 0.5,
what is the population regression function?
y =
(b)
Use the regression function in part (a) to determine the mean yield (in percent) for a plot planted on May 8 with a density of 41,182 plants/ha. (Round your answer to two decimal places.)
%
(c)
Would the mean yield be higher for a planting date of May 8 or May 22 (for the same density)?
The mean yield would be higher for .
(d)
Is it…
The variable income (yearly) is examined in a regression setting where the predictor variable is lag (1) of income and the following output is produced.
a) Write down the regression equation.
b) Interpret the meaning of the slope.
c) A dummy variable for gender (male=0, female=1) was added to the model. Interpret its coefficient of -0.2.
2. A sample of small cars was selected to attempt to use the horsepower (x) in hp of the car
to predict the fuel efficiency (y) in miles per gallon. A researcher fitted a linear regression
model.
ŷ-44.0 -0.150x
a) Interpret the slope of the regression line.
b) Find the predicted fuel efficiency for a horsepower of 150 hp?
c) If the fuel efficiency for a car of horsepower of 150hp had an actual fuel efficiency of
25mpg, what is the residual (error) for this car?
d) Calculate the correlation coefficient.
e) What is the strength of the correlation coefficient?
R²=68%
f) Interpret the y-intercept.
Chapter 14 Solutions
Introduction to Statistics and Data Analysis
Ch. 14.1 - Prob. 1ECh. 14.1 - The authors of the paper Weight-Bearing Activity...Ch. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - The relationship between yield of maize (a type of...
Ch. 14.1 - Prob. 11ECh. 14.1 - A manufacturer of wood stoves collected data on y...Ch. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - State as much information as you can about the...Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - The ability of ecologists to identify regions of...Ch. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - Prob. 28ECh. 14.2 - The article The Undrained Strength of Some Thawed...Ch. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - This exercise requires the use of a statistical...Ch. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Prob. 38ECh. 14.3 - Prob. 39ECh. 14.3 - The article first introduced in Exercise 14.28 of...Ch. 14.3 - Data from a random sample of 107 students taking a...Ch. 14.3 - Benevolence payments are monies collected by a...Ch. 14.3 - Prob. 43ECh. 14.3 - Prob. 44ECh. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Exercise 14.26 gave data on fish weight, length,...Ch. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - The article The Analysis and Selection of...Ch. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Prob. 57ECh. 14.4 - Prob. 58ECh. 14.4 - Prob. 59ECh. 14.4 - Prob. 60ECh. 14.4 - This exercise requires use of a statistical...Ch. 14.4 - Prob. 62ECh. 14 - Prob. 63CRCh. 14 - Prob. 64CRCh. 14 - The accompanying data on y = Glucose concentration...Ch. 14 - Much interest in management circles has focused on...Ch. 14 - Prob. 67CRCh. 14 - Prob. 68CRCh. 14 - Prob. 69CRCh. 14 - A study of pregnant grey seals resulted in n = 25...Ch. 14 - Prob. 71CRCh. 14 - Prob. 72CRCh. 14 - This exercise requires the use of a statistical...
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