A researcher performs an experiment, changing the value of the independent variable x and recording values of the dependent variable y. She calculates the value of the correlation coefficient to be r=0.7r=0.7

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: If the correlation between X and Y is r = 0.00, then the regression equation, Y = bx + a, will have…

A: The provided information is as follows:The given example is related to linear regression and the…

Q: The coefficient of determination of a set of data points is 0.862 and the slope of the regression…

A: From the given information, The coefficient of determination, r2= 0.862 Slope of the regression…

Q: The table below gives the number of hours seven randomly selected students spent studying and their…

A: Hours Studying 0.5 1 1.5 2 3 3.5 4.5 Midterm Grades 63 66 68 72 74 93 94

Q: The table below gives the number of hours seven randomly selected students spent studying and their…

A: Hours Studying(x) Midterm Grades(y) 1 72 2.5 78 3 83 3.5 91 4 95 4.5 96 5 97

Q: The table below gives the number of hours spent unsupervised each day as well as the overall grade…

A: The data values are as follow: Hours Unsupervised (x) 1 2 2.5 3.5 4 5.5 6 Overall Grades (y) 99…

Q: Study investigators collect standardized data on timed 24 hr urinary excretion for 10,079 men and…

A: (a) Interpret the coefficient of determination. The coefficient of determination is interpreted…

Q: The table below gives the number of hours seven randomly selected students spent studying and their…

A: N=7 Hours Studying 1 1.5 2 2.5 3 3.5 4.5 Midterm Grades 61 62 75 77 79 83 88

Q: Step 4 of 6: According to the estimated linear model, if the value of the independent variable is…

A: The equation of regression line is ŷ= bo + bx Where bo is Y intercept And b1 is slope

Q: From a regression equation r = 0.71 and the slope = 3.5. What is the linear correlation coefficient…

A: Given : r² = 0.71 slope = 3.5

Q: The coefficient of determination of a set of data points is 0.784 and the slope of the regression…

A: The following information has been provided: The coefficient of determination is R2=0.784. The slope…

Q: The coefficient of determination of a set of data points is 0.837 and the slope of the regression…

A: r2=0.837 slope=m=3.26

Q: e table below gives the number of hours spent unsupervised each day as well as the overall grade…

Q: Imagine that you do a correlation on some X/Y data and you find the following values: Mx = 9, My =…

A: Given Mx = 9, My = 13, SSx = 80, SSy = 90, SP = +35.

Q: For a certain data set the regression equation is y = 21 - 8x. The correlation coefficient between y…

A: y=21-8x

Q: he table below gives the number of hours spent unsupervised each day as well as the overall grade…

A: The independent variable is Hours Unsupervised. The dependent variable is Overall Grades. This is…

Q: A set of n = 25 pairs of X and Y values has a correlation of r = -0.50 with SSX = 38 and SSY = 14.…

A: Given, n = 25 r = -0.50 SSX = 38 SSY = 14

Q: de (CO2), in ppm. What temperature would you expect if CO2 concentration was 300 ppm? Also, what…

A: the given regression equation is temperature = 10.5 + 0.0109 CO2 the R2 = 79.6% to find i)…

Q: In a simple linear regression model, the correlation coefficient between x and y is 0.8. What can…

A: The question is about correlation Given : Value of correlation coefficient ( r ) = 0.8 To find :…

Q: An amusement park sales director is interested in predicting the number of beverages purchased based…

A: Here an amusement park sales director is interested in predicting the number of beverages purchased…

Q: = The table below gives the number of hours spent unsupervised each day as well as the overall grade…

A: We have given that, The data set are :- Hours unsupervised (X) :- 1.5, 2, 3, 4, 5, 5.5, 6 Overall…

Q: You run a regression analysis and obtain the regression equation y = 1.784x 22.666 with a…

A: Formula for predicted response value (Y) Y= bX + a Where X is explanatory variable

Q: The following table gives the data for the average temperature and the snow accumulation in several…

A: The data shows average temperatures and snow accumulations.

Q: The table below gives the number of hours spent unsupervised each day as well as the overall grade…

A: Coefficient of determination is denoted by r2

Q: In performing regression analysis between the age of a car and the cars value, you calculate the…

A: To answer this question we have to know 1.What is correlation 2.Types of correlation and…

Q: The coefficient of determination of a set of data points is 0.842 and the slope of the regression…

A: Introduction: In this case, the coefficient of determination is 0.842, and the slope of the…

Q: The table below gives the number of hours spent unsupervised each day as well as the overall grade…

A: here, data given for 7 students. Therefore, n = 7. The slope is estimated as follows:…

Q: Hours Unsupervised 0 1 3 4 5 Overall Grades 95 92 85 81 62 Table Step 6 of 6 : Find the value…

A: (X) : { 0,1,3,4,5 } (Y) : { 95,92,85,81,62 } Here : X = hours Unsupervised Y = Overall Grades…

Q: Step 4 of 6: Find the estimated value of y when x = Answer How to enter your answer (opens in new…

A: Given that X Y X \cdot YX⋅Y X^2X2 Y^2Y2 36 336 12096 1296 112896 52 335 17420 2704…

Q: A football coach is looking for a way to identify players that are "under weight". The coach decides…

A: Given: The provided regression equation is:…

Q: The table below gives the number of hours spent unsupervised each day as well as the overall grade…

A: Given data and calculation is shown below Hours(x) Grades(y) x2 y2 xy 0 87 0 7569 0 1 86 1…

Q: The table below gives the number of hours seven randomly selected students spent studying and their…

A: The data is defined below as follows: From the information, given that

Q: The table below gives the age and bone density for five randomly selected women. Using this data,…

A: Given : Let age be x and Bone density be y X Y 47 360 49 353 50 336 51 333 58 310

Q: The table below gives the number of hours seven randomly selected students spent studying and their…

A: The data is defined below as follows: From the information, given that

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

A researcher performs an experiment, changing the value of the independent variable x and recording values of the dependent variable y. She calculates the value of the correlation coefficient to be r=0.7r=0.7 and draws the associated regression line. What percentage of the variation in y cannot be attributed to changes in x and the associated relationship indicated on the regression line?

Definition Definition Statistical measure used to assess the strength and direction of relationships between two variables. Correlation coefficients range between -1 and 1. A coefficient value of 0 indicates that there is no relationship between the variables, whereas a -1 or 1 indicates that there is a perfect negative or positive correlation.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Correlation, Regression, and Association$

Learn more about

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

Similar questions

A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation r, then find r^2.) Does the regression equation account for a significant portion of the variance in GPA? Use α = .05 to evaluate the F-ratio.
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y = bo + b,x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 1 1.5 2.5 4 4.5 Overall Grades 97 93 85 74 72 71 66 Table Copy Data Step 3 of 6: Find the estimated value of y when x = 4.5. Round your answer to three decimal places.
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y = bo + bx, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 1 1.5 3 4 4.5 5.5 Overall Grades 87 86 79 78 76 67 65 Table Copy Data Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places. Prev AnswerHow to enter your answer (opens in new window) E Tables E Keypad Keyboard Shortcuts © 2021 Hawkes Learning UIS A
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y = bo + b,x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 1 1.5 2.5 3.5 5.5 Overall Grades 96 94 89 87 82 74 68 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. 田 Tables E Keypad Answer Keyboard Shortcuts How to enter your answer Submit Answer © 2021 Hawkes Learning to search hp
The least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Interpret the slope.
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y = bo + b,x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0.5 2 3 4.5 Overall Grades 99 98 96 92 89 88 80 Table Copy Data Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age 37 40 52 60 67 Bone Density 352 351 336 329 319. Find the estimated slope. Round your answer to three decimal places
Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 4.5), (2, 6.0), (4, 8.4), (6, 11.7), (8, 16.2)} ŷ = r =
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, y = bo + b₁x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, In practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age Answer How to enter your answer (opens in new window) Bone Density 40 61 62 68 69 357 350 343 340 315 Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places. Tables Copy Data Keypad Keyboard Shortcuts Table Previous step answers Submit Answer Dec 3 4:51 VI
A researcher collected data on people's heights and their shoe sizes from 500 people (N=500). Then, she convert the two variables (X-: heig ht, Y: shoe size) to standard scores before computing regression constants and the correlation coefficient between the two variables. The correlation coefficient (from the standardized scores) was found to be r = .37. Which of the following statements is CORRECT? a. Although the correlation coefficient is positive (r=.37), the regression slope can be negative O b. If the correlation coefficient was computed from raw scores, it will not be r=.37 O c. The regression slope (from the standardized scores) is the same as the correlation coefficient (r=.37) Od. The Y-intercept (from the standardized scores) is the same as the correlation coefficient (r=.37)
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were:y=ax+b a=-1.38 b=39.555 r2=0.693889 r=-0.833 Assume the correlation is significant, and use this to predict the number of situps a person who watches 7 hours of TV can do (to one decimal place)
When the heights (in inches) and shoe lengths (also in inches) were measured for a large random sample of individuals, it was found that r = 0.89, and a regression equation was constructed in order to further explore the relationship between shoe length and height, with height being the response variable. From this information, what can we conclude? The correlation coefficient should have no units. The regression equation relating shoe length to height must have a slope equal to 0.89. The regression equation relating shoe length to height must have a positive intercept. O Approximately 89% of the variability in height can be explained by the regression equation. Because the value of r is less than 1, we should characterize this relationship as being weak.