CORRELATION COEFFICIENT
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1) Correlation between x and y is 0.52, their covariance is 7.8. If the variance of x is 16, then S.D of y is: A 2.85. B) 3.25. C) 1.25. D) 3.75
2) Find r if ∑x=50, ∑y=100, ∑x²=255, ∑y²=4594, ∑xy=630,n=10
A) 0.8678. B) 0.9698 C) 0. 9688. D) None
3) Find r if ∑x=125, ∑y=100, ∑x²= 650, ∑y²=436, ∑xy=520,n=25 A) 0.667. B) - 0.667
C) 1.667. C) 0.0667
4) Find r, n=8 ∑x=56, ∑y=40, ∑x²=524, ∑y²= 256, ∑xy= 364.
5) Find r if n=10, ∑x=140,∑y=150,
∑(x-10)²=180, ∑=(y-15)²=215,
∑(x-10)(y-15)=60
a) 0.81 b) 0.91 c) -0.81 d) -0.91
6) find r if n=12, ∑x=120, ∑y=130,
∑(x-8)²=150, ∑(y-10)²= 200,
∑(x-8)(y-10)= 50
a) 0.215 b) -0.215 c) -0.317 d) n
7) Find r if
¹²ᵢ₌₁∑(x - mean of x)²=120,
¹²ᵢ₌₁∑(y- mean of y)²=250 ,
¹²ᵢ₌₁∑(x-mean of x)(y-mn of y) = 225.
a) 0.987 b) -0.75 c) 0.75 d) 0.85
8) If cov(x,y)=12, r=0.6 and s.d of
x=5 find s.d of y.
a) 2 b) 3 c) 1 d) 4
9) If r=0.5, ∑uv=120,∑u²=90 and σᵥ=8 find n
a) 8 b) 9 c) 10 d) 12
10) cov (u,v)=3, σ²ᵤ= 4.5, σ²ᵥ=5.5, find r.
a) +0.503 b) +0.603
c) -0.603 d) -0.556
11) Find the probable error of r if
r=0.05 and n=25.
a) 0.1928 b) 0.1292
c) 0.0129 d) 0.0192
12) If r= +0.526 and n=50, what is the probable of r.
a) 0.06623 b) 0.6623
c) 1.6623 d) - 0.6629
13) ¹⁰⁰ᵢ₌₁∑x=280, ¹⁰⁰ᵢ₌₁∑y=60,
¹⁰⁰ᵢ₌₁∑x²=2384, ¹⁰⁰ᵢ₌₁∑y²=117,
¹⁰⁰ᵢ₌₁∑xy=438. find
i) Correlation coefficient
a) 0.45 b) 0.75 c) 0.95 d) 1
ii) Coefficient of determination.
a) 0.0456 b) 0.9556
c) 0.5625 d) 0.2595
iii) The percentage of variation unaccounted for is
a) 43.85% b) 56.25%
c) 65.52% d) none
iv) standard error of r is
a) 0.04234 b) 0.05784
c) 0.03585 c) 0.04375
v) Probable error of r is.
a) 0.02951 b) 0.29515
c) 0.95411 d) none
14) X: 1 2 3 4 5
Y: 3 2 5 4 6 find r.
a) 0.45 b) 0.8 c) 0.95 d) 1.00
15) X: 1 2 3 4 5.
Y: 6 8 11 8 12 Find r.
a) +0.775 b) - 0.775
c) + 0.895 d) + 0.956
16) X: 10 12 13 16 17 20 25
Y: 19 22 24 27 29 33 37
find correlation Coefficient.
a) -0.987 b) 0.99 c)0.895 d) -0.99
17) You are given the following data relating to aptitude scores(x) and productivity index(y).
x- 9 18 18 20 20 23
y- 33 23 33 42 29 32
Find the co-efficient of correlation between aptitude and productivity index.
a) 0.3333 b) 0.0237
c) 0.0337 d) 0.0733
18) Find correlation coefficient
X- 4 6 8 10 12
Y- 3 6 9 12 15
a) +1 b) - 1 c) 0 d) +0.878
19) Find r taking 44 and 26 as the
origin of X and Y
X Y
43 29
44 31
46 19
40 18
44 19
42 27
45 27
42 29
38 41
40 30
42 26
57 10
a) -0.73 b) +0.73
c) -0.537 d) +0.537
20) Calculate correlation between age and playing habits of students from the data given .
age(yrs) no. of regular
students players
15 250 200
16 200 150
17 150 90
18 120 48
19 100 30
20 80 12
a) - 0.0963 b) + 0.096
c) - 0.1963 d) + 0.0963
21) What can be said about the coefficient of correlation .
X 1 2 3 4 5 6 7
Y 3 5 6 8 10 11 13
a) r is greater than 0
b) X ,Y are positively correlated
c) r= 1 - 0.0028 d) none
22) In order to find the correlation coefficient between X and Y where n=12, ∑x=30, ∑y=5, ∑x²=670, y²=285, ∑xy=334. On subsequent verification it was found that the pair (11,4) was copied wrongly, the correct value being(10,14). find correct correlation coefficient.
a) -0.87 b) -0.78 c) 0.87 d) 0.78
23) In order to find the correlation coefficient between X and Y where n=25, ∑x=125, ∑y=100, ∑x²=650, y²=460, xy= 508. On subsequent verification it was found that (6,14) and (8,6) was copied wrongly, the correct value being(8,12) and (6,8). find correct correlation coefficient.
a) 0.76 b) 0.67 c) -0.756 d) -0.678
24) For bivariate data, there exist many types of relationship between the variables?
a) one b) two c) three d) more
25) If the data are collected for two variables simultaneously, it is known as:
a) Univariate Data.
b) Biveriate Data
c) Conditional Data
d) Marginal Data
26) The frequency distribution related to two variables collected at the same point of time is known as :
a) Bivariate Frequency Distri.
B) Joint frequency distribution
C) two-way frequency distribution
D) all of the above
27) From the Bivariate Frequency Distribution, we can obtain which of the following Univariate distribution ?
A) Marginal distribution
B) Conditional distribution
C) both A and B above
D) neither A nor B above
28) The total number of cells in (m+n) bivariate frequency table are :
A) m+n. B) m -n. C) m. D) mn
29) In a bivariate frequency distribution, if there m classification for x and n classification for y, then there would be altogether ___ conditional distribution.
A) m+n. B) m -n. C) m. D) mn
30) In (m+n) bivariate frequency table, the maximum number of marginal distribution is:
A) 1. B) 2. C) No marginal distribution exists. D) m+n.
31) In (m+n) bivariate distribution table, some of the cell frequencies may be:
A) Zero. B) negative.
C) Both A and B above. D) none
32) For which of the following statements the correlation will be negative ?
A) production and price unit.
B) sale of woolen garments and day temperature.
C) Only A above
D) Both A and B above
33) Which of the following is the example of variables Which are uncorrelated ?
A) Profit & Investment
B) Price & Demand of an item.
C) Shoe-size & Intelligence.
D) Yield & Rainfall.
34) Karl Pearson's correlation coefficient may be defined as:
A) The ratio of covariance between the two variables to the product of the standard deviations of the two variables.
B) The ratio of covariance between the two variables to the product of the variance of the two variables.
C) The ratio of product of standard deviations of the two variables to the covariance between the two variables.
D) none
35) If the value of "r" is "+". then there is a____correlation between the variables.
A) negative. B) positive
C) both negative and positive
D) neither positive nor negative.
36) If r=0, then there is____ correlation between the two variables.
A) negative. B) positive. C) No
D) both positive and negative.
37) If the variables are inversely proportional to each other, then statistically they are__ correlated.
A) positively. B) not
C) negatively. D) none
38) Which of the following statements are valid?
A) positive value of correlation between x and y implies that if x decreases, y tends increase.
B) Correlation coefficient is independent of the origin of reference but is dependent on the units of measurement.
C) Correlation coefficient between u and v turned out to be -1.02
D) none
39) Product moment Correlation coefficient, can measure Correlation when the variables are having which type (s) of relation?
A) non-linear. B) linear
C) curvilinear. D) both A and B
40) ___ is the simple way of the diagrammatic representation of bivariate data.
A) Time Series Graph.
B) Radar Diagram
C) Frequency Polygon
D) Scatter Diagram
41) The scatter diagram gives us the ___ ideas about the Correlation between the two variables
A) exact. B) Vague. C) No.D) none
42) Scatter Diagram can be applied for___ Correlation.
A) linear. B) Curvilinear
C) A as well as B above
D) Only B above
43) Scatter Diagram fails to:
A) Distinguish between different types of Correlation.
B) Measure the extent of relationship between the variables
C) Both A and B above. D) none
44) On a scatter diagram if one is not able to recognise a specific pattern, then the two variables depicts_____ Correlation.
A) no. B) positive. C) both negative and positive
D) perfectly negative.
45) Which of the following regarding value of "r" is TRUE ?
A) "r" is a pure number
B) "r" lies between-1 and+1
C) Only B is true
D) Both A and B are true
46) Which of the following regarding value of "r" is TRUE ?
A) 0 and 1. B) - 1 and 0
C) - 1 and+1. D) none
47) ____ Correlation coefficient is a measure of reliability.
A) standard error.
B) statistical error
C) probable error
D) both A and C above
48) Coefficient of Determination is:
A) square of Correlation
B) cube of Correlation
C) square root of Correlation
D) none
49) Standard Error of "r" is given by:
A) (1 - r²)/n. B) (1-r²)/√n
C) (1+r²)/√n. D) none
50) Probable error of r is how many times the standard error of r
A) 6.745.B) 67.C)0.6745 d) 0.4765
51) Coefficient of non-determination is :
A) r². B) 1+r². C) 1 - r². D) 1
52) The ratio of coefficient of non- determination and the square root of the number of variables is known as:
A ) Probable error. B) error
C) standard error. D) none
53) Find Correlation coefficient
X: 2 3 5 8 9
Y: 4 6 10 16 18
A) 1 B) 0 C) -1 D) none
54) If r ˣʸ = 0.6, what will be the value of rᵤᵥ , where u = 3x +5 and v= 4y -3
a) -0.6 b) 0.6 c) 0.36 d) none
55) If r ˣʸ = 0.6, what will be the value rᵤᵥ , where u= 3x+5 and v=-4y+3
a) -0.6 b) 0.6 c) 0.36 d) 0.66
56) U= 2X +11 and V= 3Y+7, What will be the Correlation coefficient between U and V ?
A) 1. B) -1. C) r ˣʸ. D) none
57) In a Correlation analysis, the values of Karl Pearson's Correlation coefficient and it's probable error were found to be 0.90 and 0.04 respectively. Find the value of n.
A) 9. B) 11. C) 10. D) 15
58) Which of the following methods to Calculate Correlation coefficient do not take into account the magnitude of the two variables?
A) Product moment method
B) Rank correlation Method
C) Concurrent deviation method
D) All of the above.
59) Which is the quickest method to find the Correlation coefficient between two variables?
A) Scatter Diagram
B) Method of concurrent deviation
C) Product Moment method
D) Spearman's Rank correlation
1) D 2) C. 3) D 4) c 5) b 6) A. 7) c. 8) d 9) c 10) b 11) b. 12) a 13) b 14) b 15) a. 16) b 17) c 18) a 19) a 20) a 21) d 22) d 23) b 24) c 25) b 26) d 27) c 28) d 29) a 30) b 31) a 32) d 33) c 34) a 35) b 36) c 37) c 38) d 39) b 40) d 41) b 42) c 43) b 44) a 45) d 46) d 47) c 48) a 49) b 50) c 51) c 52) c 53) a 54) b 55) a 56) c 57) c 58) c 59) a
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