Find the coefficient of correlation from the following data: x 2 3 5 7 3 y 15 17 4 5 4

Given that, the data is x 2 3 5 7 3 y 15 17 4 5 4 We know that, correlation coefficient r = ∑ x i - x ¯ y i - y ¯ ∑ x i - x ¯ 2 ∑ y i - y ¯ 2 ⇒ Mean of x values is x ¯ = 2 + 3 + 5 + 7 + 3 5 = 4 ⇒ Mean of y values is y ¯ = 15 + 17 + 4 + 5 + 4 5 = 9 x y x i - x ¯ y i - y ¯ x i - x ¯ 2 y i - y ¯ 2 x i - x ¯ y i - y ¯ 2 15 - 2 6 4 36 - 12 3 17 - 1 8 1 64 - 8 5 4 1 - 5 1 25 - 5 7 5 3 - 4 9 16 - 12 3 4 0 - 5 0 25 0 Σ x = 20 Σ y = 45 Σ x i - x ¯ = 1 Σ y i - y ¯ = 0 Σ x i - x ¯ 2 = 15 Σ y i - y ¯ 2 = 166 Σ x i - x ¯ y i - y ¯ = - 37 ⇒ r = - 37 15 166 = - 0 . 74

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Calculate the Karl Pearson’s coefficient of correlation for the following data and interpret.(Answer up to two decimal values)

$\begin{matrix} x & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ y & 15 & 16 & 14 & 13 & 11 & 12 & 10 & 8 & 9 \end{matrix}$

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Important Questions on Correlation Analysis

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Find the coefficient of correlation from the following data:

$x$	$2$	$3$	$5$	$7$	$3$
$y$	$15$	$17$	$4$	$5$	$4$

MEDIUM

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

If scatter diagram from a line move from lower left to upper right corner then the correlation is______.

MEDIUM

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

If the equation of the two regression lines are

2 x - 3 y = 0

and

4 y - 5 x = 8

then the correlation coefficient between

x

and

y

is equal to______.

MEDIUM

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Y = 9 X

and

X = 0.01 Y

, then

r

is equal to:

MEDIUM

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Consider to regression line

3 x + 2 y = 26, 6 x + y = 31

. Find the correlation coefficient between

x

and

y

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

If the correlation coefficient between

x

and

y

0.5

then Find the correlation coefficient between

2 x - 3

and

3 - 5 y

is:

MEDIUM

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Find correlation coefficient:

$X$	$5$	$4$	$3$	$2$	$1$
$Y$	$1$	$2$	$3$	$4$	$5$

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Prove that : Value of correlation coefficient

r

lies between

- 1 to + 1

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Find the coefficient of correlation from the regression lines:

x - 2 y + 3 = 0 and 4 x - 5 y + 1 = 0

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Product moment coefficient of correlation is

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

______ measures the degree of relationship between two variables.

HARD

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Calculate the covariance of the following bivariate data :

$X$	$48$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
$Y$	$78$	$72$	$66$	$60$	$54$	$48$	$42$	$36$	$30$	$24$	$18$	$12$

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Rank correlation was developed by

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

______ presents a description of quantitative relation between two series of facts.

MEDIUM

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Find the covariance of the data given below :

(1, 5), (2, 7), (3, 9), (4, 11), (5, 10), (6, 9), (7, 8), (8, 7), (9 . 6), (10, 5)

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

If the regression coefficients are

0.8

and

0.2

, then the value of the coefficient of correlation is

MEDIUM

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Calculate the covariance of observations $(3, 5), (6, 7), (9, 9), (12, 11) (15, 13), (18, 15), (21, 17), (24, 19)$ , using assumed means $A = 13$ and $B = 12$ .

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

The correlation coefficient of two variable

x

and

y

0.8

. The regression coefficient of

y

x

0.2

, then the regression coefficient of

x

y

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Rank correlation coefficient is given by

EASY

Mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

If cov (x, y) = 0 then its interpretation is

Calculate the Karl Pearson’s coefficient of correlation for the following data and interpret.(Answer up to two decimal values) x987654321y1516141311121089

Important Questions on Correlation Analysis

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Calculate the Karl Pearson’s coefficient of correlation for the following data and interpret.(Answer up to two decimal values)

$\begin{matrix} x & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ y & 15 & 16 & 14 & 13 & 11 & 12 & 10 & 8 & 9 \end{matrix}$