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
131
In the linear regression equation Y = a + bX, what does the constant 'a' represent?
Answer:
Y-intercept
In the simple linear regression equation Y = a + bX, 'a' represents the Y-intercept, which is the value of Y when X is equal to zero. It indicates the starting point of the regression line on the vertical axis. The coefficient 'b' represents the slope of the line, indicating the change in Y for a unit change in X.
132
What is the standard formula for calculating the Spearman's rank correlation coefficient for non-tied data?
Answer:
$$1 - \frac{{6\sum {D^2}}}{{N\left( {{N^2} - 1} \right)}}$$
The Spearman rank correlation coefficient (rho) measures the strength and direction of the association between two ranked variables. The formula 1 - (6 * sum(D^2)) / (N * (N^2 - 1)) is derived from the Pearson correlation coefficient applied to ranks. It is specifically used when there are no tied ranks in the data, where D represents the difference between the ranks of corresponding pairs.
133
What is the formula for Spearman's rank correlation coefficient when tied ranks are present in the dataset?
Answer:
$$1 - \frac{{6\left[ {\sum {D^2} + \frac{1}{{12}}\left( {{m^3} - {m_1}} \right) + \frac{1}{{12}}\left( {{m^3} - {m_2}} \right) + .....} \right]}}{{{N^3} - N}}$$
When ranks are tied, the standard Spearman formula must be adjusted. The correction factor involves adding (m^3 - m)/12 for each set of tied ranks, where m is the number of items sharing a rank. This adjustment accounts for the reduction in variance caused by ties, ensuring the correlation coefficient remains accurate within the range of -1 to +1.
134
In the context of regression analysis, what is the nature of the relationship assumed to exist between the dependent variable and the independent variable?
Answer:
dependent
Regression analysis is a statistical method used to model and analyze the relationship between variables. Specifically, it examines how the value of a dependent variable changes when one or more independent variables are varied. The core assumption is that the dependent variable is functionally related to the independent variable(s) being studied.
135
Identify the false statement regarding regression and correlation analysis.
Answer:
Coefficient of correlation is independent of origin but not of scale
The coefficient of correlation is a dimensionless measure. It is mathematically independent of both the change of origin and the change of scale. Therefore, the statement that it is not independent of scale is false. The other statements correctly describe the properties of regression and correlation coefficients.
136
If the sum of two variables X and Y remains constant for all observations, what is the coefficient of correlation between them?
Answer:
-1 (perfectly negative)
If X + Y = C (a constant), then Y = C - X. This represents a linear relationship with a negative slope of -1. Therefore, as X increases, Y must decrease by the exact same amount, resulting in a perfect negative correlation of -1.
137
Determine the type of correlation between the two variates X (1, 2, 3, 4, 5, 6) and Y (10, 12, 14, 16, 18, 20).
Answer:
+1
As X increases by 1 unit, Y increases by 2 units consistently. Since the variables move in the same direction at a constant rate, there is a perfect positive linear correlation, represented by a correlation coefficient of +1.
138
Given Σx = 440, Σy = 330, Σx² = 17,986, Σy² = 10,366, Σxy = 13,467, and n = 11, what is the Pearson correlation coefficient (r) rounded to two decimal places?
Answer:
0.63
The correlation coefficient is calculated using the formula r = [nΣxy - (Σx)(Σy)] / sqrt([nΣx² - (Σx)²][nΣy² - (Σy)²]). Substituting the provided values: numerator = (11*13467) - (440*330) = 148137 - 145200 = 2937. Denominator = sqrt((11*17986 - 440²)*(11*10366 - 330²)) = sqrt((197846-193600)*(114026-108900)) = sqrt(4246 * 5126) = sqrt(21765000) ≈ 4665.3. r = 2937 / 4665.3 ≈ 0.63.
139
What term describes a functional relationship between two variables?
Answer:
Regression Analysis
Regression analysis is a statistical method used to estimate the relationships between variables. It focuses on the relationship between a dependent variable and one or more independent variables, allowing for prediction and modeling.
140
What are the primary applications or utilities of correlation analysis in business and research?
Answer:
All of the above
Correlation analysis is a versatile statistical tool. It identifies the strength and direction of relationships between variables, which is essential for academic research. Furthermore, understanding these relationships allows managers to make informed predictions and strategic decisions based on observed trends.