a. Explanation Given info: The data are given as, x –5 –3 –1 1 2 5 y –32 –60 –80 –92 –96 –92 The equation is given as y = x 2 − 6 x − 87 Calcualtion: Linear correlation coefficient: The linear correlation coefficient for n data points is given as, r = 1 n − 1 ∑ i ( x i − x ¯ ) ( y i − y ¯ ) s x s y Where s x and s y denote the sample standard deviations of the x– values and y – values , respectively . The computing formula for linear correlation coefficient is, r = ∑ i x i y i − ( ∑ i x i ) ( ∑ i y i ) ∑ i x i 2 − ( ∑ i x i ) 2 / n ∑ i y i 2 − ( ∑ i y i ) 2 / n A positive value of r indicates variables are positively correlated, a negative value of r indicates variables are negatively correlated and if r is zero then there is no linear relationship between the variables b. To determine Explain ether it is possible to conclude from the answer in part a. that the variables x and y are unrelated. c. To determine Draw a scatterplot for the data. d. To determine Explain whether the data is appropriate in use of the linear correlation coefficient as a descriptive measure. e. To determine Show the data are related by the quadratic equation y = x 2 − 6 x − 87 . f. To determine Graph the equation and the data points.

10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

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 14.4, Problem 152E

To determine

Compute the linear correlation coefficient r.

To determine

Explain ether it is possible to conclude from the answer in part a. that the variables x and y are unrelated.

To determine

Draw a scatterplot for the data.

To determine

Explain whether the data is appropriate in use of the linear correlation coefficient as a descriptive measure.

To determine

Show the data are related by the quadratic equation y=x2−6x−87.

To determine

Graph the equation and the data points.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 151E

Chapter 14.4, Problem 153E

Students have asked these similar questions

1 - Multiple Regression Equations and Predictions with XLMiner Analysis ToolPak (Structured) Video The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks are entered into the Microsoft Excel Online file below. Use the XLMiner Analysis ToolPak to perform your regression analysis in the designated areas of the spreadsheet. Due to a recent change by Microsoft you will need to open the XLMiner Analysis ToolPak add-in manually from the home ribbon. Screenshot of ToolPak X Open spreadsheet a. Develop an estimated regression equation with the amount of television advertising as the independent variable (to 2 decimals). JAN 27 Revenue = × TVAdv + b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables (to 2 decimals). Revenue = + TVAdy + NewsAdv c. Is the estimated regression equation coefficient for…

Question 2: When John started his first job, his first end-of-year salary was $82,500. In the following years, he received salary raises as shown in the following table. Fill the Table: Fill the following table showing his end-of-year salary for each year. I have already provided the end-of-year salaries for the first three years. Calculate the end-of-year salaries for the remaining years using Excel. (If you Excel answer for the top 3 cells is not the same as the one in the following table, your formula / approach is incorrect) (2 points) Geometric Mean of Salary Raises: Calculate the geometric mean of the salary raises using the percentage figures provided in the second column named “% Raise”. (The geometric mean for this calculation should be nearly identical to the arithmetic mean. If your answer deviates significantly from the mean, it's likely incorrect. 2 points) Hint for the first part of question 2: To assist you with filling out the table in the first part of the question,…

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile range, variance, and standard deviation (to a maximum of 2 decimals, if decimals are necessary). Range Interquartile range Variance Standard deviation

Chapter 14 Solutions

Introductory Statistics (10th Edition)

Ch. 14.1 - Regarding linear equations with one independent...Ch. 14.1 - Prob. 2E Ch. 14.1 - Consider the linear equation y = b0 + b1x. a....Ch. 14.1 - Prob. 4E Ch. 14.1 - In Exercises 14.514.14, we give linear equations....Ch. 14.1 - Prob. 6E Ch. 14.1 - In Exercises 14.5-14.14, we give linear equations....Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - In Exercises 14.514.14, we give linear equations....

Knowledge Booster

$Statistics$

Learn more about

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

Compute the linear correlation coefficient r .

Solution Summary: The author calculates the linear correlation coefficient r for n data points.

Concept explainers

Videos

Compute the linear correlation coefficient r.

Explain ether it is possible to conclude from the answer in part a. that the variables x and y are unrelated.

Draw a scatterplot for the data.

Explain whether the data is appropriate in use of the linear correlation coefficient as a descriptive measure.

Show the data are related by the quadratic equation y=x2−6x−87.

Graph the equation and the data points.

Want to see the full answer?

Chapter 14 Solutions