An aerobic exercise instructor remembers the data given in the following table, which shows the recommended maximum exercise heart rates for individuals of the given ages. (A graphing calculator is recommended.) Age (x years) 20 40 60 Maximum heart rate 165 148 131 (y beats per minute) (a) Find the linear correlation coefficient for the data. (Round your answer to two decimal places.) (b) What is the significance of the value found in part (a)? O One of the data points is the y-intercept. O The graph of the regression points passes through none of the data points. O The slope of the regression is about half of what the expected value is. O The linear correlation coefficient should always be positive. O The graph of the regression points passes through all three data points. (c) Find the equation of the least-squares regression line. (Round your answers to two decimal places.)
An aerobic exercise instructor remembers the data given in the following table, which shows the recommended maximum exercise heart rates for individuals of the given ages. (A graphing calculator is recommended.) Age (x years) 20 40 60 Maximum heart rate 165 148 131 (y beats per minute) (a) Find the linear correlation coefficient for the data. (Round your answer to two decimal places.) (b) What is the significance of the value found in part (a)? O One of the data points is the y-intercept. O The graph of the regression points passes through none of the data points. O The slope of the regression is about half of what the expected value is. O The linear correlation coefficient should always be positive. O The graph of the regression points passes through all three data points. (c) Find the equation of the least-squares regression line. (Round your answers to two decimal places.)
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 11CT
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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:An aerobic exercise instructor remembers the data given in the following table, which shows the recommended maximum exercise heart rates for individuals of the given ages. (A graphing calculator is recommended.)
Age (x years)
20
40
60
Maximum heart rate
165
148
131
(y beats per minute)
(a) Find the linear correlation coefficient for the data. (Round your answer to two decimal places.)
(b) What is the significance of the value found in part (a)?
O One of the data points is the y-intercept.
O The graph of the regression points passes through none of the data points.
O The slope of the regression is about half of what the expected value is.
O The linear correlation coefficient should always be positive.
O The graph of the regression points passes through all three data points.
(c) Find the equation of the least-squares regression line. (Round your answers to two decimal places.)
(d) Use the equation of the least-squares line from part (c) to predict the maximum exercise heart rate for a person who is 74. (Round your answer to the nearest whole number.)
beats per minute
(e) Is the procedure in part (d) an example of interpolation or extrapolation?
O extrapolation
O interpolation
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