a. Explanation Formula used: The correlation coefficient, r = n ( ∑ x y ) − ( ∑ x ) ( ∑ y ) ( n ( ∑ x 2 ) − ( ∑ x ) 2 ) ( n ( ∑ y 2 ) − ( ∑ y ) 2 ) . Calculation: Let x be the systolic blood pressure readings and y be the diastolic blood pressure readings. The number of observations is 6. So, n is 6. Compute the values of x 2 , y 2 and x y as shown below in Table 1 x x 2 y y 2 x y 110 ( 110 ) 2 = 12 , 100 70 ( 70 ) 2 = 4 , 900 ( 110 ) ( 70 ) = 7 , 700 153 ( 153 ) 2 = 23 , 409 110 ( 110 ) 2 = 12 , 100 ( 153 ) ( 110 ) = 16 , 830 120 ( 120 ) 2 = 14 , 400 80 ( 80 ) 2 = 6 , 400 ( 120 ) ( 80 ) = 9 , 600 143 ( 143 ) 2 = 20 , 449 98 ( 98 ) 2 = 9 , 604 ( 143 ) ( 98 ) = 14 , 014 100 ( 100 ) 2 = 10 , 000 70 ( 70 ) 2 = 4 , 900 ( 100 ) ( 70 ) = b. To determine Whether the correlation exists at α = 0.05 or not for the given data. c. To determine The equation of the line of best fit for the systolic blood pressure and the diastolic blood pressure readings. d. To determine To estimate: The diastolic blood pressure for an adult with a systolic blood pressure reading of 115.

A Survey of Mathematics with Applications (10th Edition) - Standalone book

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Author: Allen R. Angel, Christine D. Abbott, Dennis Runde

Publisher: PEARSON

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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.

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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.

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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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Chapter 12.6, Problem 40E

To determine

The correlation coefficient between the systolic blood pressure and the diastolic blood pressure readings.

To determine

Whether the correlation exists at α=0.05 or not for the given data.

To determine

The equation of the line of best fit for the systolic blood pressure and the diastolic blood pressure readings.

To determine

To estimate: The diastolic blood pressure for an adult with a systolic blood pressure reading of 115.

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Chapter 12.6, Problem 39E

Chapter 12.6, Problem 41E

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The correlation coefficient between the systolic blood pressure and the diastolic blood pressure readings.

Solution Summary: The author explains the correlation coefficient between the systolic blood pressure and the diastolic readings, which is 0.984.

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The correlation coefficient between the systolic blood pressure and the diastolic blood pressure readings.

Whether the correlation exists at α=0.05 or not for the given data.

The equation of the line of best fit for the systolic blood pressure and the diastolic blood pressure readings.

To estimate: The diastolic blood pressure for an adult with a systolic blood pressure reading of 115.

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Chapter 12 Solutions