Commerce MCQs
Topic Notes: Commerce
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
101
Match the following.List-I(Terms)List-II(Definitions)a. Simple regression1. Process of predicting one variable from anotherb. Multiple regression2. Single variable is used to predict another variable on the assumption of linear relationship between the given variablesc. Simple linear regression analysis3. Involves two or more independent variables and one dependent variable
Answer:
a-1, b-3, c-2
Source answer preserved: option B (a-1, b-3, c-2). AI attempted to change protected answer data (option_a, option_b, option_c, option_d), so this item is flagged for manual review before study use.
102
Calculate the coefficient of correlation given that the two regression coefficients are 0.8 and 0.2.
Answer:
+ 0.40
The correlation coefficient (r) is the geometric mean of the two regression coefficients (bxy and byx). Mathematically, r = ±√(bxy * byx). Here, r = √(0.8 * 0.2) = √0.16 = 0.4. Since both regression coefficients are positive, the correlation coefficient must also be positive, resulting in +0.40.
103
What is the range of the coefficient of correlation?
Answer:
Varies between ± 1
The Pearson correlation coefficient, denoted as 'r', measures the strength and direction of a linear relationship between two variables. Its value is mathematically constrained to fall within the inclusive range of -1 to +1. A value of +1 indicates a perfect positive linear relationship, while -1 indicates a perfect negative linear relationship, and 0 indicates no linear correlation.
104
Evaluate the following statements: Assertion (A) states that if the regression coefficient of X on Y exceeds one, the regression coefficient of Y on X must be less than one. Reason (R) states that the geometric mean of two regression coefficients equals the correlation coefficient.
Answer:
(A) and (R) are correct
The product of the two regression coefficients (bxy * byx) equals the square of the correlation coefficient (r^2). Since r^2 cannot exceed 1, if one coefficient is greater than 1, the other must be less than 1 to keep the product within the range of 0 to 1. Furthermore, the geometric mean of the two coefficients is indeed equal to the correlation coefficient, confirming both statements.
105
What is the standard formula for calculating the probable error of the correlation coefficient?
Answer:
0.6745 S.E.
The probable error (P.E.) of the Pearson correlation coefficient is used to measure the reliability of the coefficient. It is calculated as 0.6745 times the standard error (S.E.) of the correlation coefficient. This constant is derived from the normal distribution properties where 50% of the distribution lies within this range.
106
How should a correlation coefficient value of 0.959 be interpreted in statistical analysis?
Answer:
Highly positively correlated
A correlation coefficient ranges from -1 to +1. A value of 0.959 is very close to +1, indicating a strong positive linear relationship between the two variables. Since it is not exactly 1, it is not 'perfectly' correlated, but rather 'highly' or 'strongly' correlated. This means that as one variable increases, the other variable is also very likely to increase in a consistent manner.
107
What term describes a scenario where all data points in a set fall exactly along a straight line?
Answer:
Linear relationship
A linear relationship exists when the change in one variable is proportional to the change in another, resulting in a straight-line pattern when plotted on a graph. If all points lie perfectly on this line, it indicates a perfect linear correlation.
108
If the coefficient of determination (R-squared) is 0.64, what is the corresponding coefficient of correlation (r)?
Answer:
0.80
The coefficient of determination, denoted as R-squared, is the square of the correlation coefficient (r). Therefore, to find r, one must take the square root of 0.64. The square root of 0.64 is 0.80. This value represents the strength and direction of the linear relationship between two variables.
109
When is a correlation between two variables considered to be linear?
Answer:
change in one variable tend to bear constant ratio of change in the other
A linear correlation exists when the relationship between two variables can be represented by a straight line. This means that for every unit change in one variable, there is a constant, proportional change in the other variable. This constant ratio of change is the defining characteristic of linearity in statistical correlation analysis.
110
Which of the following are recognized methods for calculating the correlation coefficient?
Answer:
(i), (ii), (v)
Correlation analysis commonly employs Karl Pearson's product-moment correlation coefficient for linear relationships, Spearman's Rank correlation for ordinal data, and the Concurrent Deviation method for assessing the direction of change. Yule's method and the Coefficient of Contingency are generally associated with association of attributes rather than standard correlation coefficients.