Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 8, Problem 7SE
To determine
Plot the residuals versus fitted line plot for the linear model, Quadratic model an cubic model.
Check for the appropriateness of the three models.
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A chemistry experiment is performed measuring the solubility of potassium chloride (KCl) in water at different temperatures. The goal was to determine if there is a linear relationship between the temperature of the water and how much KCl can dissolve, measured as grams per 100 milliliter (g/100mL).
After the experiments were performed, the following data was collected with temperature being the independent x-variable and solubility being the dependent y-variable:
Temperature (°C)
x
Solubility (g/100mL)
y
10
31
20
33
30
37
40
41
50
42
Based on the data given for temperature and solubility of KCl and without doing any math yet, which of the following do you predict would best describe the relationship between these variables?
A positive linear relationship (r close to 1)
A positive linear relationship (r close to -1)
A negative linear relationship (r close to 1)
A negative linear relationship (r close to -1)…
In a comprehensive road test on new car models, one variable measured is the time it takes a car to accelerate from 0 to 60 miles per hour.
To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars.
TIME60: y = Elapsed time (in seconds) from 0 mph to 60 mph
MAX: x = Maximum speed attained (miles per hour)
The simple linear model E(y) = Bo + B1x was fit to the data. Computer printouts for the analysis are given below:
NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60
PREDICTOR
VARIABLES COEFFICIENT STD ERROR STUDENT'S T
CONSTANT
187171
0.63708
29.38
0.0000
0.0000
MAX
-0.08365
0.00491
-17.05
0.6960
0.6937
R-SQUARED
RESID. MEAN SQUARE (MSE)
1.28695
ADJUSTED R-SQUARED
STAND ARD DEVIATION
113444
SOURCE
DF
MS
F
REGRESSION
374.285
0.0000
374.285
1.28695
290.83
RESIDUAL
127
163.443
TOTAL
128
537.728
CASES INCLUDED 129 MISSING CASES 0
Fill in the blank: "At a =.05, there is
between maximum speed and acceleration time."
O sufficient evidence of a…
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.
Chapter 8 Solutions
Statistics for Engineers and Scientists
Ch. 8.1 - In an experiment to determine the factors...Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - The article Application of Analysis of Variance to...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Refer to Exercise 7. a. Find a 95% confidence...Ch. 8.1 - In a study of the lung function of children, the...Ch. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - The following MINITAB output is for a multiple...Ch. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - The following data were collected in an experiment...Ch. 8.1 - The November 24, 2001, issue of The Economist...Ch. 8.1 - The article Multiple Linear Regression for Lake...Ch. 8.1 - Prob. 19ECh. 8.2 - In an experiment to determine factors related to...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.3 - True or false: a. For any set of data, there is...Ch. 8.3 - The article Experimental Design Approach for the...Ch. 8.3 - Prob. 3ECh. 8.3 - An engineer measures a dependent variable y and...Ch. 8.3 - Prob. 5ECh. 8.3 - The following MINITAB output is for a best subsets...Ch. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - (Continues Exercise 7 in Section 8.1.) To try to...Ch. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - The article Ultimate Load Analysis of Plate...Ch. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - The article Modeling Resilient Modulus and...Ch. 8.3 - The article Models for Assessing Hoisting Times of...Ch. 8 - The article Advances in Oxygen Equivalence...Ch. 8 - Prob. 2SECh. 8 - Prob. 3SECh. 8 - Prob. 4SECh. 8 - In a simulation of 30 mobile computer networks,...Ch. 8 - The data in Table SE6 (page 649) consist of yield...Ch. 8 - Prob. 7SECh. 8 - Prob. 8SECh. 8 - Refer to Exercise 2 in Section 8.2. a. Using each...Ch. 8 - Prob. 10SECh. 8 - The data presented in the following table give the...Ch. 8 - The article Enthalpies and Entropies of Transfer...Ch. 8 - Prob. 13SECh. 8 - Prob. 14SECh. 8 - The article Measurements of the Thermal...Ch. 8 - The article Electrical Impedance Variation with...Ch. 8 - The article Groundwater Electromagnetic Imaging in...Ch. 8 - Prob. 18SECh. 8 - Prob. 19SECh. 8 - Prob. 20SECh. 8 - Prob. 21SECh. 8 - Prob. 22SECh. 8 - The article Estimating Resource Requirements at...Ch. 8 - Prob. 24SE
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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…arrow_forwardA new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960.arrow_forwardThe electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature ( x1 ), the number of days in the month ( x2 ), the average product purity ( x3 ), and the tons of product produced ( x4 ). The past year’s historical data are available and are presented in the following table:regression model is y = -102.7132 + 0.6054X1 + 8.9236X2 + 1.4374 X3 + 0.0136X4 a) Estimate sigma^2b.) Using ANOVA, test for significance of regression using α=0.05. Determine the critical value of the test statistic (2 decimal places only). c.) Using ANOVA, test for significance of regression using α=0.05. Determine the computed value of the test statistic d) Calculate R^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %). e) Calculate R_adj^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %).f) Test the significance of x3 at α=0.05. Determine the value of the test statistic. g)…arrow_forward
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