Question:
In statistical analysis of numerical data, which ONE or MORE among the options is/are possible value(s) of correlation coefficient?
In statistical analysis of numerical data, which ONE or MORE among the options is/are possible value(s) of correlation coefficient?
Show Hint
The correlation coefficient always lies between -1 and 1; check which options fall outside this range.
Updated On: Aug 3, 2026
- 0
- 10.3
- -0.9
- 2
Show Solution
Verified By Collegedunia
The Correct Option is A, C
Solution and Explanation
Step 1: Recall the definition and range of the correlation coefficient:
The correlation coefficient, usually written as r, measures how strongly two numerical variables move together in a straight line relationship.
By definition, it is a normalised quantity, and this normalisation forces it to always lie between -1 and 1.
\[ -1 \le r \le 1 \]
Step 2: Understand what the extreme and middle values mean:
When r equals 1, the two variables increase together perfectly, that is a perfect positive linear relationship.
When r equals -1, one variable increases exactly as the other decreases, a perfect negative linear relationship.
When r equals 0, there is no linear relationship at all between the two variables.
No real value of r can ever step outside this closed interval, no matter how the data is arranged.
Step 3: Test each option against this range:
Option (A), 0, lies right in the middle of the interval, so it is a valid value.
Option (B), 10.3, is far greater than 1, so this can never be a correlation coefficient.
Option (C), -0.9, lies between -1 and 1, close to the negative end, so it is a valid value.
Option (D), 2, is greater than 1, so this is also impossible.
Final Answer:
Only values that stay within -1 and 1 can be correlation coefficients, so 0 and -0.9 qualify. \[ \boxed{0 \text{ and } -0.9} \]
The correlation coefficient, usually written as r, measures how strongly two numerical variables move together in a straight line relationship.
By definition, it is a normalised quantity, and this normalisation forces it to always lie between -1 and 1.
\[ -1 \le r \le 1 \]
Step 2: Understand what the extreme and middle values mean:
When r equals 1, the two variables increase together perfectly, that is a perfect positive linear relationship.
When r equals -1, one variable increases exactly as the other decreases, a perfect negative linear relationship.
When r equals 0, there is no linear relationship at all between the two variables.
No real value of r can ever step outside this closed interval, no matter how the data is arranged.
Step 3: Test each option against this range:
Option (A), 0, lies right in the middle of the interval, so it is a valid value.
Option (B), 10.3, is far greater than 1, so this can never be a correlation coefficient.
Option (C), -0.9, lies between -1 and 1, close to the negative end, so it is a valid value.
Option (D), 2, is greater than 1, so this is also impossible.
Final Answer:
Only values that stay within -1 and 1 can be correlation coefficients, so 0 and -0.9 qualify. \[ \boxed{0 \text{ and } -0.9} \]
Was this answer helpful?
0
0
Top GATE PI Engineering Mathematics Questions
- In the Taylor series expansion of sin z around \(z = 0\), the coefficient of the term \(z^3\) is
- A vector field is given as \(F(x, y) = (100x + 100y) i + (−50x + 200y) j\), where \(i\) and \(j\) are the unit vectors along the \(x\) and \(y\) axes in the Cartesian frame, respectively. Then the value of
\(∮F(x, y). dl\)
where \(dl = dx i + dy j\) is an elemental path taken over an anticlockwise circular contour \(C\) of radius \(r = 2\) is
- A uniform cantilever beam of length L and flexural rigidity EI is loaded by a force F as shown in the figure. Assuming that the Euler-Bernoulli beam theory is applicable here, the magnitude of the static deflection at the free end of the beam is
- In a complex function
\(f(x, y) = u(x, y) + i v(x, y),\)
\(i\) is the imaginary unit, and \(x, y, u(x, y)\) and \(v(x, y)\) are real.
If \(f(x, y)\) is analytic then which of the following equations is/are TRUE? - If \(X\) is a continuous random variable with the probability density function
\(f(x) = \begin{cases} \frac K4 & ; 0\leq x \leq 1\\ 0 & ; \text{otherwise} \end{cases}\)
Then the value of \(K\) is _____ . (Answer in integer)
View More Questions
Top GATE PI Probability and Statistics Questions
- For a given process control chart, there are four rules for determining out-of-control state of the process which are being used simultaneously. The probability of Type-I error for the four rules are 0.005, 0.02, 0.03, and 0.05. Assuming independence of the rules, the probability of overall Type-I error when all the four rules are used simultaneously is
- The probability mass function \( P(x) \) of a discrete random variable \( X \) is given by \( P(x) = \frac{1}{2^x} \), where \( x = 1, 2, \dots, \infty \). The expected value of \( X \) is _________.
- The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 15 minutes. The probability that the passenger will miss the flight is _________.
\text{[round off to 3 decimal places]} - A box in a machine shop consists of 5 coated and 10 uncoated cutting inserts which are of otherwise similar characteristics. The inserts got mixed up randomly in the box. An operator has taken 4 of them at once without noticing the differences to mount on a 4-tooth face milling cutter that uses inserts.
The probability of the milling cutter having all uncoated inserts is ______ (rounded off to two decimal places). - The number of soldering defects that occur in a semiconductor device follows a discrete Poisson distribution with a probability mass function
\[ p(x) = \frac{e^{-\lambda}\lambda^x}{x!} \]
The average number of soldering defects per semiconductor device is 3.
The probability that a randomly selected semiconductor device will have at least two soldering defects is ______ (rounded off to two decimal places).
Top GATE PI Questions
- In an air-standard Otto cycle, the pressure and temperature of air just before the compression stroke are 200 kPa and 26.85 °C, respectively. The combustion process is assumed to be a constant volume process, where 1.02 MJ/kg heat is added. The cycle efficiency is 50%. The adiabatic index \(γ\) and specific heat at constant volume \(C_v\) can be considered to be constant during the process (corresponding values taken at the mean cycle temperature).
Assuming that the ideal gas law is applicable, \(γ = \frac 43\) and \(c_v= 0.85\ kJ/kg-K\), the maximum pressure (in MPa) reached during the cycle is _____ . (Rounded off to 1 decimal place) - A metallic cylindrical pressure vessel, used to store compressed air in a plant, has 1 m mean radius and 4 mm wall thickness. The maximum allowable normal and shear stresses in the cylindrical portion of the vessel are 100 MPa and 40 MPa, respectively. Considering only these data in the design, the maximum allowable internal gauge pressure (in MPa) of the compressed air is ______ . (Rounded off to 2 decimal places)
- A flat belt drive with pulley of r = 20 cm radius is designed to transmit 6.283 kW power at 600 RPM. In the figure, τ is the corresponding torque. If the coefficient of static friction between the belt and the pulley is 0.3, then the minimum value of the tightening force F (in kN) required to prevent the belt slip is _____ . (Rounded off 2 decimal places)
- Mild steel plates are welded to make butt joints by arc welding with 85% heat transfer efficiency ignoring other losses. The first weld joint is made by selecting arc voltage of 30 V and current of 180 A with a welding speed of 6 mm/s. Using identical plates, a second weld joint is made with the same arc voltage and a welding speed of 8 mm/s. If both the welds have the same heat input, then the welding current (in A) for the second weld joint is _____. (Answer in integer)
- In a single pass cold rolling operation, a flat plate is reduced to a thickness of 3 mm. In this operation, two rolls of diameter 400 mm each are rotating in opposite direction at 300 RPM, and the elastic deflection of these rolls is negligible. The angle of bite is 10°. If the neutral point is present at an angle of 7° from the exit side, then the thickness of the plate (in mm) at the neutral point is _____ . (Rounded off to 1 decimal place)
View More Questions