An aerobic exercise instructor remembers the data given in the following table, which shows the recommended maximum exercise heart rates for individuals given ages. (A graphing calculator is recommended.) Age (x years) 20 40 60 Maximum heart rate 170 153 136 (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 none of the data points. O One of the data points is the y-intercept. O The graph of the regression points passes through all three data points. O The linear correlation coefficient should always be positive. O The slope of the regression is about half of what the expected value is.

An aerobic exercise instructor remembers the data given in the following table, which shows the recommended maximum exercise heart rates for individuals given ages. (A graphing calculator is recommended.) Age (x years) 20 40 60 Maximum heart rate 170 153 136 (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 none of the data points. O One of the data points is the y-intercept. O The graph of the regression points passes through all three data points. O The linear correlation coefficient should always be positive. O The slope of the regression is about half of what the expected value is.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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

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
170
153
136
(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)?
The graph of the regression points passes through none of the data points.
One of the data points is the y-intercept.
The graph of the regression points passes through all three data points.
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 Iline. (Round your answers to two decimal places.)
ŷ =
(d) Use the equation of the least-squares line from part (c) to predict the maximum exercise heart rate for a person who is 71. (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 interpolation
O extrapolation

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