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Correlation - Class 11 Commerce Economics - Extra Questions

Define the positive co-relation.



For the given lines of regression, 3x2y=5 and x4y=7, find:
coefficient of correlation r(x,y)



From the equation of the two regression lines, 4x+3y+7=0 and 3x+4y+8=0, find: Coefficient of correlation.



Prove that coefficient of correlation lies between 1 and 1.



Find the coefficient of correlation from the following data.
x23573
y1517454



Calculate coefficient of correlation from the following data: 
xy
315
1017
84
65
84



Calculate the correlation coefficient between x and y for the following data:
x59131721
y1220253335



If "r" is a coefficient of correlation of two variables x and y, then prove that:
r=σ2x+σ2yσ2xy2σx.σy Where σ2x,σ2y and σ2xy are the variance of x,y and xy respectively.



Find the coefficient of correlation from the following data.
x1050510
y5971113



Calculate the Spearman's ranks correlation coefficient for the following data and interpret the result:
X35548095737335918381
Y40607590707538957570



For a bivariate data bYX=1.2 and bXY=0.3, find the correlation coefficient between x and y.



If Cov(x,y)= 1125, Ox= 47.5, and Oy= 39.Find r.



Calculate the coefficient of correlation between X and Y series from the following data:
n=15,¯x=25,¯y=18,σX=3.01,σY=3.03,(xi¯x)(yi¯y)=122.



If d2i=25, n=6 find rank correlation coefficient where di is the difference between the ranks of ith values.



If the rank correlation coefficient is 0.6 and the sum of squares of difference of ranks is 66, then find the number pairs of observations.



Find out Spearman's rank correlation:

X

Y

20

60

11

63

72

26

65

35

43

43

29

51

50

37



Interpretate the value of coefficient of correlation (r) lies between -1 to 1.



Find the value of correlation from the following information:

Price (Rs.)

PPE kit (supply)

500

25

700

35

800

40

1000

50

1100

55

1200

60

1400

70

1500

75

1800

90

2000

100



The two lines of regressions are x+2y5=0 and 2x+3y8=0 and the variance of x is 12. Find the variance of y and the coefficient of correlation.



In a contest the competitors are awarded marks out of 20 by two judges. The scores of the 10 competitors are given below. Calculate Spearman's rank correlation.
CompetitorsABCDEFGHIJ
Judge A2111118658161315
Judge B611169142431317



The two lines of regressions are 4x+2y3=0 and 3x+6y+5=0. Find the correlation coefficient between x and y.



A psychologist selected a random sample of 22 students. He grouped them in 11 pairs so that the students in each pair have nearly equal scores in an intelligence test. In each pair, one student was taught by method A and the other by method B and examined after the course. The marks obtained by them after the course are as follows:
Pairs1234567891011
Method A2429191430192730202811
Method B3735162623271920161121
Calculate Spearman's Rank correlation



The following results were obtained with respect to two variable x and y:
x=30,y=42,xy=199,x2=184,y2=318,n=6. Find the correlation coefficient between x and y.



For 10 pairs of observation on two variables x and y, the following data are available.
(x2)=30,(y5)=40,(x2)2=900.
(y5)2=800,(x2)(y5)=480.
Find the correlation coefficient between x and y



The following table shows the mean and standard deviation of the marks of Mathematics and Physics scored by the students in a school
MathematicsPhysics
Mean8481
Standard Deviation74
The correlation coefficient between the given marks is 0.86. Estimate the likely marks in Physics if the marks in Mathematics are 92.



For 10 points of observations on two variables X and Y, the following data are available:
(x2)=30,y5=40,(x2)2=900
(y5)2=800,(x2)(y5)=480.
Find the correlation coefficient between X and Y.



The equations of the two regression line are 2x+3y6=0 and 5x+7y12=0
Find
(a) Correlation coefficient
(b)  σxσy



Calculate coefficient of correlation from the following data and interpret the result.
Number of Years of Schooling of Farmers03691215
Annual Yield per Acre (in '000)668121210



Calculate coefficient of correlation for the ages of husband and wife.
Age of Husband (X)242522303437
Age of Wife (Y)202118262830



Class 11 Commerce Economics Extra Questions