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
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y
10
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41
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A negative linear relationship (r close to 1)
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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.
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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
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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_forwardThe 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 and the independent variables. y = 2 % x₁ and X4 y = a + B₁x₁ + B₂×2 + B3×3 + B4x4 + e (a) If a = 21.08, B₁ = 0.652, B₂ = 0.0023, B3 = -0.0208, and 4 = 0.2, what is the population regression function? = O No, since there are other terms involving X₁. O Yes, since there are other terms involving X₁. O Yes, since there are no other terms involving X₁. x₂ provides a good description of the relationship between y (b) Use the regression function in part (a) to determine the mean yield (in percent) for a plot planted on May 3 with a density of 41,178 plants/ha. (Round you answer to two decimal places.) (c) Would the mean yield be higher for a planting…arrow_forward1. By applying the least coefficients method (linear regression) to the table values below;a) Draw a straight line.b) Find the y value for x=30.arrow_forward
- The 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_forwardA certain puppy when born weighs 8 pounds, and its weight increases linearly by 0.45 pounds per day for the first week. Construct a model for the puppy’s weight during the first week using the variables W for weight and d for days.arrow_forward
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