An aerobic exercise instructor remembers the data given In the following table, which shows the recommended maximum exercise heart rates for Individuals of the ages. (A graphing calculator Is recommended.) Age (x years) 20 40 60 Maximum heart rate 174 159 144 (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 The graph of the regression points passes through all three data points. O The graph of the regression points passes through none of the data points. O One of the data points is the y-Intercept. O The linear correlation coefficient should always be positive. O The slope of the regression is about half of what the expected value is. (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 ages. (A graphing calculator Is recommended.) Age (x years) 20 40 60 Maximum heart rate 174 159 144 (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 The graph of the regression points passes through all three data points. O The graph of the regression points passes through none of the data points. O One of the data points is the y-Intercept. O The linear correlation coefficient should always be positive. O The slope of the regression is about half of what the expected value is. (c) Find the equation of the least-squares regression line. (Round your answers to two decimal places.)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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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

The average remaining lifetimes for women of various ages in a certain country are given in the following table. (A graphing calculator is recommended.)
Average Remaining
Lifetimes for Women
Age (x)
Years (y)
0.
79.2
15
66.5
35
46.0
65
18.7
75
11.5
(a) Find the equation of the least-squares line for the data. (Round all numerical values to two decimal places.)
(b) Use the equation from part (a) to estimate the remaining lifetime of a woman of age 27. (Round your answer to the nearest year.)
yr
(c) Is the procedure in part (b) an example of interpolation or extrapolation?
interpolation
extrapolation

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
174
159
144
(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 The graph of the regression points passes through all three data points.
The graph of the regression points passes through none of the data points.
One of the data points is the y-intercept.
The linear correlation coefficient should always be positive.
The slope of the regression is about half of what the expected value is.
(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 70. (Round your answer to the nearest
whole number.)
beats per minute
(e) Is the procedure in part (d) an example of interpolation or extrapolation?
Oextrapolation
interpolation

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