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
1
What is the implication when a linear regression line passes directly through the origin (0,0)?
Answer:
Intercept is zero
The general equation for a linear regression line is Y = a + bX, where 'a' represents the y-intercept. If the line passes through the origin, it means that when X is zero, Y must also be zero. Substituting these coordinates into the equation (0 = a + b(0)) confirms that the intercept 'a' must be zero.
2
In regression analysis, what is the process of verifying whether the underlying assumptions of the model are valid called?
Answer:
significance analysis
Regression analysis relies on several assumptions, such as linearity, homoscedasticity, and normality of errors. Significance analysis is often used to test the validity of these assumptions and the reliability of the coefficients. While specification analysis is also relevant for checking model structure, significance testing is the standard term used to determine if the observed relationships are statistically meaningful and not due to random chance.
3
Given the values ∑xy = 40, N = 100, ∑x² = 80, and ∑y² = 20, what is the calculated correlation coefficient?
Answer:
+1.0
The correlation coefficient (r) is calculated using the formula r = ∑xy / sqrt(∑x² * ∑y²). Substituting the given values: r = 40 / sqrt(80 * 20) = 40 / sqrt(1600) = 40 / 40 = 1.0. Thus, the result is +1.0, indicating a perfect positive linear correlation between the two variables.
4
Evaluate the following assertion and reason regarding linear relationships between variables: Assertion (A): A linear relationship between two variables does not necessarily imply an independent-dependent relationship. Reason (R): Causal relationships between variables may not always be supported by a sound theoretical framework.
Answer:
Both (A) and (R) are true and (R) is the correct explanation
Correlation measures the strength of a linear relationship but does not prove causation. Two variables may show a high correlation due to a third lurking variable or mere coincidence. Therefore, a statistical linear relationship does not automatically establish a cause-and-effect link. The reason provided correctly identifies that statistical association requires a robust theoretical basis to claim causality, making the assertion and reason logically connected.
5
In statistical terms, what degree of dispersion indicates that all data points lie exactly on a regression line?
Answer:
one
In the context of correlation and regression analysis, a correlation coefficient of 1 (or -1) indicates a perfect linear relationship. When the degree of dispersion is zero relative to the line of best fit, all data points fall perfectly on that line. The provided answer 'one' likely refers to the correlation coefficient magnitude, implying perfect linear alignment. Dispersion measures how spread out data points are from the mean or a trend line.
6
Which one of the following formulae is used to calculate probable error of correlation coincident between two variables of 'n' pairs of observations?
Answer:
$$0.6745\left[ {\frac{{1 - {r^2}}}{{\sqrt n }}} \right]$$
Source answer preserved: option A ($$0.6745\left[ {\frac{{1 - {r^2}}}{{\sqrt n }}} \right]$$). 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.
7
The intersecting point of two regression lines is
Answer:
$$\overline x ,\,\overline y $$
Source answer preserved: option B ($$\overline x ,\,\overline y $$). AI attempted to change protected answer data (option_b), so this item is flagged for manual review before study use.
8
Given the regression equations x = 0.85y and y = 0.89x, what is the calculated value of the coefficient of correlation?
Answer:
0.87
The coefficient of correlation (r) is the geometric mean of the two regression coefficients (bxy and byx). Here, bxy = 0.85 and byx = 0.89. Therefore, r = sqrt(0.85 * 0.89) = sqrt(0.7565) which is approximately 0.8697. Rounding this value gives 0.87, which matches option A.
9
What does the linear equation Y = A + BX represent in statistical analysis?
Answer:
Regression line of Y on X
The equation Y = A + BX is the standard form for the regression line of Y on X, where Y is the dependent variable, X is the independent variable, A is the intercept, and B is the slope coefficient. This model predicts the value of Y based on a given value of X.
10
Karl Pearson's correlation coefficient is calculated by which of the following formula?
Answer:
$$\frac{{{\text{Covariance of X and Y}}}}{{\sqrt {{\text{Var}}{\text{.}}\left( {\text{X}} \right)\,{\text{Var}}{\text{.}}\left( {\text{Y}} \right)} }}$$
Source answer preserved: option B ($$\frac{{{\text{Covariance of X and Y}}}}{{\sqrt {{\text{Var}}{\text{.}}\left( {\text{X}} \right)\,{\text{Var}}{\text{.}}\left( {\text{Y}} \right)} }}$$). 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.