Explanation Given: The given xy pairs are (3, 5), (7, 8), (4, 6), (6, 7). Definition used: If we have pairs of data for two variables x and y , the linear correlation coefficient for these data, denoted by r , is given by the formula r = n ∑ x y − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 n ( ∑ y 2 ) − ( ∑ y ) 2 , where n is the number of pairs of data we have for x and y . Calculation: Consider the given xy pairs. The computations to calculate correlation coefficient is shown below x y xy x 2 y 2 3 5 15 9 25 7 8 56 49 64 4 6 24 16 36 6 7 42 36 49 ∑ x = 20 ∑ y = 26 ∑ x y = 137 ∑ x 2 = 110 ∑ y 2 = 174 Substitute the known values in r = n ∑ x y − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 n ( ∑ y 2 ) − ( ∑ y ) 2

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

See similar textbooks

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 p…

Videos

Question

Chapter 14.5, Problem 7E

To determine

To find:

Whether we can be 95% or 99% confident that there is significant linear correlation between x and y.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 6E

Chapter 14.5, Problem 8E

Students have asked these similar questions

Step 5. Calculate the correlation coefficient.

A scientist, who wants to study the effects of precipitation on rice crops, sets up an experiment with 4 groups of rice crops. Rice crop harvest vs. precipitation level Group B Group A 0 150 Group C Precipitation (cm/annually) Harvest (pounds/acre) 0 60 Which statement best describes the relationship between the dependent and independent variables in this study? 20 O The amount of precipitation is dependent on the amount of rice harvest. O The amount of rice harvest is positively correlated with the increase in precipitation. The amount of rice harvest is not affected by the amount of precipitation. The amount of rice harvest is negatively correlated with the increase in precipitation. 200 Group D 40 300

The data in the table can be entered into a calculator to determine a linear equation of best fit where x represents the elapsed time in minutes and y represents the depth of water in a tub in inches. What conclusion can be drawn from the correlation coefficient? A There is a weak positive correlation between the variables. B There is a weak negative correlation between the variables. C There is a strong positive correlation between the variables. D There is a strong negative correlation between the variables.

Chapter 14 Solutions

Mathematics All Around (6th Edition)

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Whether we can be 95% or 99% confident that there is significant linear correlation between x and y .

Solution Summary: The author explains that they can be 95% or 99% confident that there is significant linear correlation between x and y.

Concept explainers

Videos

To find:

Whether we can be 95% or 99% confident that there is significant linear correlation between x and y.

Want to see the full answer?

Chapter 14 Solutions

Whether we can be 95% or 99% confident that there is significant linear correlation between x and y .

Solution Summary: The author explains that they can be 95% or 99% confident that there is significant linear correlation between x and y.

Concept explainers

Videos

To find: Whether we can be 95% or 99% confident that there is significant linear correlation between x and y.

Want to see the full answer?

Chapter 14 Solutions

To find:

Whether we can be 95% or 99% confident that there is significant linear correlation between x and y.