Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305445963
Author: PECK
Publisher: Cengage
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Chapter 14.2, Problem 31E
To determine
Test whether the quadratic model is useful to specify the relationship between y and x or not at 0.01 level of significance.
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A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a
regression analysis was performed, and a portion of the computer output is as follows:
ŷ = 4.5+ 14.4x
Coefficients
(Intercept)
x
Estimate
4.5
Ho: B₁ = 0
H₁: B₁ > 0
Ho: B₁ = 0
Ha: B₁ <0
14.4
Ho: B₁ = 0
Ha:
B₁ #0
Std. Error Test statistic
2.9
4.7
1.55
3.06
P-value
Specify the null and the alternative hypotheses that you would use in order to test whether a linear
relationship exists between x and y.
0.07
0
The relationship between yield of maize, date of planting, and planting density was investigated in an article. Let the variables be defined as follows.
y = percent maize yield
x = planting date (days after April 20)
z = planting density (plants/ha)
The following regression model with both quadratic terms where x₁ = x, X₂ = Z, X3 = x² and x4 = 2² provides a good description of the relationship between y and
the independent variables.
y =a +B₁x₁ + B₂X₂ + B3X3+B₁x₁ + e
(a) If a = 21.07, B₁ = 0.653, B₂ = 0.0022, B3 = -0.0207, and B4 = 0.00002, what is the population regression function?
y = 509
X
(b) Use the regression function in Part (a) to determine the mean yield for a plot planted on May 7 with a density of 41,182 plants/ha. (Give the exact
answer.)
(c) Would the mean yield be higher for a planting date of May 7 or May 23 (for the same density)?
The mean yield would be higher for [May 7
You may need to use the appropriate table in Appendix A to answer this question.
The authors of the paper "Predicting Yolk Height, Yolk Width, Albumen Length, Eggshell Weight, Egg Shape Index, Eggshell Thickness, Egg Surface Area of Japanese Quails Using Various Egg Traits as Regressors"t used a multiple regression model with two independent variables where
y = quail egg weight (g),
X, = egg width (mm), and
X2
= egg length (mm).
The regression function suggested in the paper is -21.658 + 0.828x,
0.373x2.
+
(a) What is the mean egg weight for quail eggs that have a width of 20 mm and a length of 48 mm? (Enter your answer to three decimal places.)
(b) Interpret the value of B,.
O When width is fixed, the mean increase in weight associated with a 1-mm increase in length is 0.373 g.
When length is fixed, the mean increase in weight associated with a 1-mm increase in width is 0.373 g.
O When length is fixed, the mean increase in weight associated with a 1-mm increase in width is 0.828 g.
O When width is fixed, the mean increase in weight associated with a 1-mm increase…
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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