2. The Great Plains Railroad is interested in studying how fuel consumption is related to the number of railcars for its trains on a certain route between Oklahoma City and Omaha. A scatterplot and residual plot from the regression analysis for these data are shown below. RESIDUALS VERSUS THE FITTED VALUES 120 110- 100 90+ 80- 70 60아 50 20 30 50 50 60 70 80 90 100 1 io 120 40 Fitted Value Number of Railcars After some calculation, we found that the correlation coefficient is r = 0.9835. Our descriptive statistics also tell us that for the Number of Railcars x, i = 35.6 and s, = 10.42. Alongside this information we also know that for Fuel Consumption y, ỹ = 87.2 and s, = 22.76. a) Using the information above, provide a brief description of the scatterplot. b) Would a linear model be appropriate for modeling these data? Explain your reasoning. c) Interpret the coefficient of determination r2. d) Suppose that s = 4.361. Interpret this value in context. e) Using the information above, construct the equation of its Least-Squares Regression Line. Fuel Consumption Residual
2. The Great Plains Railroad is interested in studying how fuel consumption is related to the number of railcars for its trains on a certain route between Oklahoma City and Omaha. A scatterplot and residual plot from the regression analysis for these data are shown below. RESIDUALS VERSUS THE FITTED VALUES 120 110- 100 90+ 80- 70 60아 50 20 30 50 50 60 70 80 90 100 1 io 120 40 Fitted Value Number of Railcars After some calculation, we found that the correlation coefficient is r = 0.9835. Our descriptive statistics also tell us that for the Number of Railcars x, i = 35.6 and s, = 10.42. Alongside this information we also know that for Fuel Consumption y, ỹ = 87.2 and s, = 22.76. a) Using the information above, provide a brief description of the scatterplot. b) Would a linear model be appropriate for modeling these data? Explain your reasoning. c) Interpret the coefficient of determination r2. d) Suppose that s = 4.361. Interpret this value in context. e) Using the information above, construct the equation of its Least-Squares Regression Line. Fuel Consumption Residual
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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Concept explainers
Correlation
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 predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Transcribed Image Text:2. The Great Plains Railroad is interested in studying how fuel consumption is related to the number of railcars
for its trains on a certain route between Oklahoma City and Omaha.
A scatterplot and residual plot from the regression analysis for these data are shown below.
RESIDUALS VERSUS THE FITTED VALUES
120-
110-
5-
100-
90+
80-
70
60-
50
20
50
60 70 80 90 100 110 120
30
40
50
Fitted Value
Number of Railcars
After some calculation, we found that the correlation coefficient is r = 0.9835. Our descriptive statistics also
tell us that for the Number of Railcars x, i = 35.6 and s, = 10.42. Alongside this information we also know
that for Fuel Consumption y, ỹ = 87.2 and s, = 22.76.
a) Using the information above, provide a brief description of the scatterplot.
b) Would a linear model be appropriate for modeling these data? Explain your reasoning.
c) Interpret the coefficient of determination r?.
d) Suppose that s = 4.361. Interpret this value in context.
e) Using the information above, construct the equation of its Least-Squares Regression Line.
Fuel Consumption
Residual
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