13th Edition

ISBN: 8220103633567

Author: Sincich

Publisher: PEARSON

Concept explainers

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Textbook Question

Chapter 12, Problem 12.159ACI

Yield strength of steel alloy. Industrial engineers at the University of Florida used regression modeling as a tool to reduce the time and cost associated with developing new metallic alloys (Modelling and Simulation in Materials Science and Engineering, Vol. 13, 2005). To illustrate, the engineers built a regression model for the tensile yield strength (y) of a new steel alloy. The potentially important predictors of yield strength are listed in the accompanying table.

x₁ = Carbon amount (% weight)

x₂ = Manganese amount (% weight)

x₃ = Chromium amount (% weight)

x₄ = Nickel amount (% weight)

x₅ = Molybdenum amount (% weight)

x₆ = Copper amount (% weight)

x₇ = Nitrogen amount (% weight)

x₈ = Vanadium amount (% weight)

x₉ = Plate thickness (millimeters)

x₁₀ = Solution treating (milliliters)

x₁₁ = Aging temperature (degrees, Celsius)

a. The engineers discovered that the variable Nickel (x₄) was highly correlated with the other potential independent variables. Consequently. Nickel was dropped from the model. Do you agree with this decision? Explain.
b. The engineers used stepwise regression on the remaining 10 potential independent variables in order to search for a parsimonious set of predictor variables. Do you agree with this decision? Explain.
c. The stepwise regression selected the following independent variables: x₁ = Carbon, x₂ = Manganese, x₃ = Chromium, x₅ = Molybdenum, x₆ = Copper, x₈ = Vanadium, x₉ = Plate thickness, x₁₀ = Solution treating, and x₁₁ = Aging temperature. All these variables were statistically significant in the step-wise model, with R² = .94. Consequently, the engineers used the estimated stepwise model to predict yield strength. Do you agree with this decision? Explain.

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Chapter 12, Problem 12.158ACI

Chapter 12, Problem 12.160ACI

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Solution Summary: The author explains that if Nickel is correlated with other independent variables in the study, then other variables can be dropped from the model.

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