An article in Technometrics (1974, Vol. 16, pp. 523–531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss (the amount of ammonia escaping) were measured with air flow x1, temperature x2, and acid concentration x3.
y = 42, 37, 37, 28, 18, 18, 19, 20, 15,14, 14, 13,11, 12, 8, 7, 8, 8, 9, 15, 15
x1= 80,80,75,62,62,62,62,62,58,58,58,58,58,58,58,50,50,50,50,50,56,70
x2= 27,27,25,24,22,23,24,24,23,18,18,17,18,19,18,18,19,19,20,20,20
x3= 89,88,90,87,87,87,93,93,87,80,89,88,82,93,89,86,72,79,80,82,91
(a) We will use R software to fit linear regression model.
R software codes
>y=c(42, 37, 37, 28, 18, 18, 19, 20, 15,14, 14, 13,11, 12, 8, 7, 8, 8, 9, 15, 15)
>x1=c(80,75,62,62,62,62,62,58,58,58,58,58,58,58,50,50,50,50,50,56,70)
>x2=c(27,27,25,24,22,23,24,24,23,18,18,17,18,19,18,18,19,19,20,20,20)
>x3=c(89,88,90,87,87,87,93,93,87,80,89,88,82,93,89,86,72,79,80,82,91)
>lm(y~x1+x2+x3)
Data vectors y, x1, x2 and x3 are created. (Please note that while creating data vector for x1 I have deleted first observation 80 because y, x2 and x3 have 21 observations each and x1 were having 22 but in order to fit regression line we must have equal number of observations for all the variables.)
lm() function is used to fit regression model.
R software output
Observe above output. Equation of fitted regression model is
= -49.15 + 0.55 x1 + 1.86 x2 - 0.06
x3 .
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An article in Technometrics (1974, Vol. 16, pp. 523–531) considered the following stack-loss data from a...
An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss (the amount of ammonia escaping) were measured with air flow X1, temperature X2, and acid concentration X3. y X1 X2 X3 42 80 27 89 37 80 27 88 37 75 25 90 28 62 24 87 18 62 22 87 18 62 23 87 19 62 24 93 20 62 24...
An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss (the amount of ammonia escaping) were measured with air flow X1, temperature X2, and acid concentration X3 . у X1 22 X3 42 80 27 89 37 80 27 88 37 75 25 90 28 62 24 87 18 62 22 87 18 62 23 87 19 62 24 93 20 62...
An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss (the amount of ammonia escaping) were measured with air flow X1, temperature x2, and acid concentration x3. y 21 .22 X3 42 80 27 89 37 80 27 88 37 75 25 90 28 62 24 87 18 62 22 87 18 62 23 87 62 24 93 19 20 62 24...
Reserve Problems Chapter 12 Section 1 Problem 11 An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss (the amount of ammonia escaping) were measured with air flow Xl, temperature X2, and acid concentration X3 X1 X2 X3 42 80 27 89 37 80 27 88 37 75 25 90 28 62 24 87 18 62 22 87 18 62 23 87...
Reserve Problems Chapter 12 Section 1 Problem 11 An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss (the amount of ammonia escaping) were measured with air flow X1, temperature x2, and acid concentration X3. y 42 80 27 89 37 80 27 88 37 75 25 90 28 62 24 87 18 62 22 87 18 62 23 87 19 62...
Reserve Problems Chapter 12 Section 1 Problem 11 An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss (the amount of ammonia escaping) were measured with air flow X[, temperature X2, and acid concentration X3 . y X X2 X3 42 80 27 89 37 80 27 88 37 75 25 90 28 62 24 87 18 62 22 87 18 62...
Reserve Problems Chapter 12 Section 1 Problem 11 An article in Technometrics (1974, Vol. 16, PP. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric add. Twenty-one daily responses of stack lass (the amount of ammonia escaping) were measured with air flow Xl, temperature.X1, and acid concentration 41 . 42 80 80 89 90 75 87 37 28 18 19 19 20 87 27 27 25 24 22 23 24 24 23 62 62 62 62...
(a) Fit a linear regression
model relating the results of the stack loss to the three regressor
variables.
Round your answers to two decimal places (e.g. 98.76).
b) Estimate σ2.
Round your answer to two decimal places (e.g. 98.76).
Reserve Problems Chapter 12 Section 1 Problem 11 Your answer is partially correct. Try again. An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of...
Twenty-one daily responses of stack loss (y) (the amount of ammonia escaping) were measured with air flow x1, temperature x2, and acid concentration x3. Obtain a matrix plot of scatter plots for all pairs of variables using Minitab, and state your conclusion based on this graph. [5 marks] Find a multiple linear regression model for this data using Minitab. [5 marks] Check the significance of the model using ANOVA via Minitab and state your conclusion at 5% alpha level. [5...
Reserve Problems Chapter 11 Section 2 Problem 1 The department of health studied the number of patients who need liver transplantation. The following data are the Liver Transplantation Waiting List (LTWL), where y is the size (in number of patients) and x is the corresponding year: 1278 1761 2917 3923 4983 6914 7655 7596 77378524 8376 8639 8946 x 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Round your intermediate answers to four decimal places...