Solution Found!
The processing of raw coal involves “washing,” in which
Chapter 7, Problem 2E(choose chapter or problem)
The processing of raw coal involves “washing,” in which coal ash (nonorganic, incombustible material) is removed. The article “Quantifying Sampling Precision for Coal Ash Using Gy’s Discrete Model of the Fundamental Error” (Journal of Coal Quality, 1989:33–39) provides data relating the percentage of ash to the volume of a coal particle. The average percentage of ash for six volumes of coal particles was measured. The data are as follows:
a. Compute the least-squares line for predicting percent ash \((y)\) from volume \((x)\). Plot the residuals versus the fitted values. Does the linear model seem appropriate? Explain.
b. Compute the least-squares line for predicting percent ash from ln volume. Plot the residuals versus the fitted values. Does the linear model seem appropriate? Explain.
c. Compute the least-squares line for predicting percent ash from \(\sqrt{\mathrm {volume}}\). Plot the residuals versus the fitted values. Does the linear model seem appropriate? Explain.
d. Using the most appropriate model, predict the percent ash for particles with a volume of 50 \(\mathrm {m^3}\).
e. Using the most appropriate model, construct a 95% confidence interval for the mean percent ash for particles with a volume of 50 \(\mathrm {m^3}\).
Equation Transcription:
Text Transcription:
(cm^3)
(y)
(x)
sqrt{volume}
m^3
m^3
Questions & Answers
QUESTION:
The processing of raw coal involves “washing,” in which coal ash (nonorganic, incombustible material) is removed. The article “Quantifying Sampling Precision for Coal Ash Using Gy’s Discrete Model of the Fundamental Error” (Journal of Coal Quality, 1989:33–39) provides data relating the percentage of ash to the volume of a coal particle. The average percentage of ash for six volumes of coal particles was measured. The data are as follows:
a. Compute the least-squares line for predicting percent ash \((y)\) from volume \((x)\). Plot the residuals versus the fitted values. Does the linear model seem appropriate? Explain.
b. Compute the least-squares line for predicting percent ash from ln volume. Plot the residuals versus the fitted values. Does the linear model seem appropriate? Explain.
c. Compute the least-squares line for predicting percent ash from \(\sqrt{\mathrm {volume}}\). Plot the residuals versus the fitted values. Does the linear model seem appropriate? Explain.
d. Using the most appropriate model, predict the percent ash for particles with a volume of 50 \(\mathrm {m^3}\).
e. Using the most appropriate model, construct a 95% confidence interval for the mean percent ash for particles with a volume of 50 \(\mathrm {m^3}\).
Equation Transcription:
Text Transcription:
(cm^3)
(y)
(x)
sqrt{volume}
m^3
m^3
ANSWER:
Step 1 of 15
(a)
Given:
(a) Let us first determine the necessary sums:
Next, we can determine 
