If $r_{x y}$ is positive the relation between X and Y is of the type

(a) when Y increases X increases

(b) when Y decreases X increases

(c) when Y increases X does not change

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Solution

(a) If r is positive the two variables move in the same direction. e.g., when the price of coffee rises, the demand for tea also rises as coffee

is a substitute for tea. Therefore, the r between the price of coffee and demand for tea will be positive.

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If r_xyis positive the relation between X and Y is of the type

(i) When Y increases X increases

(ii) When Y decreases X increases

(iii) When Y increases X does not change

\begin{matrix} C o l u m n I & C o l u m n I I P . (C_{2} H_{5})_{3} X N + C H_{3} C O O H Y & 1. C o n d u c t i v i t y d e c r e a s e s a n d t h e n i n c r e a s e s Q . K I (0.1 M) X + A g N O_{3} Y (0.01 M) & 2. C o n d u c t i v i t y d e c r e a s e s a n d t h e n d o e s n o t c h a n g e m u c h R . C H_{3} C O O H X + K O H Y & 3. C o n d u c t i v i t y i n c r e a s e s a n d t h e n d o e s n o t c h a n g e m u c h S . N a O H X + H I Y & 4. C o n d u c t i v i t y d o e s n o t c h a n g e m u c h a n d t h e n i n c r e a s e s \end{matrix}

List-A	List-B
(P) $(C_{2} H_{5})_{3} N X + C H_{2} C O O H Y$	(1) Conductivity decreases and then increases
(Q) $K I (0.1 M) X + A g N O_{3} (0.01 M) Y$	(2) Conductivity decreases and then does not change much
(R) $C H_{2} C O O X + K O H Y$	(3) Conductivity increases and then does not change much
(S) $N a O H X + H I Y$	(4) Conductivity does not change much and then increases.