While calculating correlation coefficient between two variables x and y from25 pairs of observations, the following results were obtained : n = 25, Ex = 125, E = 650,Ey = 100, Ey = 460, Exy = 508. Later it was discovered at the time of checking that the pairs ofvalues 3y were copied down as x8 12y. Obtain the correct value of correlation coefficient.6 14

The formula to calculate the correlation coefficient is given by…

Answered: While calculating correlation…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The following statement contains an error. Choose the statement that best explains the error. "The correlation between shoe size and height is 0.87 inches" A. Correlation requires that both of the variables be categorical B. When stating the correlation coefficient, one must state whether it is a positive or negative relationship C. This statement does not tell us whether or not shoe size is correlated with height D. When reporting correlation, one does not report units because correlation has no units E. There is no error in this statement
If the linear association between two numerical variables is studied and the correlation coefficient is 0.32, it can be concluded that:a. The relationship between the variables is inverse and weak. b. The percentage of variability observed in the data that is explained by the error is 89.76%. c. The percentage of observed variability in the data that is explained by the model is 32%. d. None is correct Please explain clearly, thank you
B). Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. C) Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot. Choose the correct answer below. A. The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope. B. The scatterplot does not reveal a distinct pattern. C. The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope. D. The scatterplot reveals a distinct pattern that is not a straight-line pattern. Clear
The following zero order correlation coefficients are given : r12 = 0.5 r13 = 0.6 r23 =.7 %3D Calculate the multiple correlation coefficients R1,23, R2.13 and R3.12
Which of the following correlation coefficients might lead a researcher to conclude that there is a weak, but significant, negative linear relation between variables X and Y? a. r=0.99 b. r=0.30 c. r=0 d. r=-0.30 c. r=-0.99
Refer to the accompanying scatterplot. a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between x and y. b. Find the value of the correlation coefficient r and determine whether there is a linear correlation. c. Remove the point with coordinates (10,10) and find the correlation coefficient r and determine whether there is a linear correlation. d. What do you conclude about the possible effect from a single pair of values? a. Do the data points appear to have a strong linear correlation? b. What is the value of the correlation coefficient for all 10 ndata points? Is there a linear correlation between x and y? Use α= 0.01. c. What is the correlation coefficient when the point(10,10)is excluded? Is there a linear correlation between x and y? Use α=0.01. d. What do you conclude about the possible effect from a single pair of values?
Match the following sample correlation coefficients with the explanation of what that correlation coefficient means. Type the correct letter in each box. 1. r= 1 2. r = -1 3. r=-.15 4. r = .1 A. a weak positive relationship between x and y B. a weak negative relationship between x and y C. a perfect negative relationship between x and y D. a perfect positive relationship between x and y
Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below. Test A (x) 43 65 73 34 99 78 65 Test B (y) 39 60 62 20 85 70 54 1. Calculate r, the linear correlation coefficient. Identify the values for each part below. Part a. The value of n Part b. The sum of the x-values Part c. The sum of the y-values Part d. The sum of the x-squared values Part e. The sum of the y-squared values Part f. The sum of the (xy) values Part g. The final value of r rounded top three decimal places
The correlation coefficient between the variables x and y is r=0.78 . If Sigma x=1.56, Sigma y=2.00, x bar=12,y bar=22 Find the equations of the registration lines Y on X
the number of rubber bands used and the distance, incentimeters, of her jump. When they created a scatterplotthe relationship appeared to be linear, and the correlationwas r = 0.996. After discussing these results, the teacherinstructed the students to convert the distances to inches.What effect will this have on the correlation between thetwo variables?a) Because 1 cm = 0.393701 inches, the correlationwill become .392126.b) Because 1 cm = 0.393701 inches, the correlationwill become 2.5298.c) Because only the length measurements have changed,the correlation will decrease substantially.d) Because changing from centimeters to inches doesnot affect the value of the correlation, the correlationwill remain 0.996. e) Because inches is a much more common measure-ment for distance in the United States, the relation-ship between the data will be stronger and thus the correlation will increase.
Which of the following measures of correlation is limited in applicability to linear relationships? Select one: а. Intraclass correlation O b. Spearman's Rho Ос. Kendall's Tau O d. Pearson
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