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
31
What term defines the amount by which the total cost changes in response to a unit change in the level of activity?
Answer:
slope coefficient
In the context of a linear cost function, the slope coefficient represents the variable cost per unit of activity. It quantifies the rate of change in the total cost for every incremental change in the activity level. Mathematically, it is the slope of the regression line, indicating how sensitive the total cost is to fluctuations in the independent variable, which is critical for effective cost management.
32
If both regression coefficients in a two-variable series are negative, what is the sign of the correlation coefficient?
Answer:
Negative
The correlation coefficient (r) is the geometric mean of the two regression coefficients (byx and bxy). Mathematically, r = ±√(byx * bxy). If both regression coefficients are negative, their product is positive, but the square root must take the sign of the regression coefficients themselves. Therefore, the correlation coefficient must be negative.
33
Between which entities can the Karl Pearson coefficient of correlation be calculated?
Answer:
Two Variables
Karl Pearson's coefficient of correlation, denoted as 'r', is a statistical measure used to quantify the linear relationship between two continuous quantitative variables. It requires numerical data for both variables to calculate the covariance and standard deviations necessary for the formula.
34
Under what condition is a positive correlation said to exist between two variables, X and Y?
Answer:
both the variables are varying in the same direction
A positive correlation occurs when two variables move in the same direction; as one variable increases, the other also increases, and as one decreases, the other decreases. This indicates a direct relationship between the variables, often represented by a positive correlation coefficient.
35
What is the mathematical range for the coefficient of correlation?
Answer:
lies between -1 and +1
The Pearson product-moment correlation coefficient, denoted by 'r', measures the strength and direction of a linear relationship between two variables. By definition, its value is constrained to the interval [-1, 1], where -1 indicates a perfect negative correlation and +1 indicates a perfect positive correlation.
36
What information can be derived from a scatter diagram of two variables X and Y?
Answer:
All of these
A scatter diagram is a graphical tool used to visualize the relationship between two variables. It helps identify the type of correlation (positive or negative), suggests potential functional relationships, and provides a visual basis for performing regression analysis to model the data.
37
Given the regression coefficients bxy = 0.25 and byx = 0.64, what is the correlation coefficient?
Answer:
0.40
The correlation coefficient (r) is the geometric mean of the two regression coefficients. It is calculated as r = sqrt(bxy * byx). Therefore, r = sqrt(0.25 * 0.64) = sqrt(0.16) = 0.40.
38
Which mathematical formula is appropriate for calculating the standard error of the coefficient of correlation for a sample size of 25?
Answer:
$$\sqrt {\frac{{1 - {r^2}}}{{n - 2}}} $$
The standard error of the correlation coefficient is used to determine the reliability of the sample correlation. The formula provided in option B is the standard statistical expression for the standard error of r, which accounts for the degrees of freedom (n-2) in the sample.
39
At what probability threshold is the slope coefficient of a beta considered to be statistically significant?
Answer:
less than 5%
In statistical hypothesis testing, a coefficient is generally considered statistically significant if the p-value is less than the chosen significance level, typically 0.05 or 5%. This indicates that there is less than a 5% probability that the observed relationship occurred by random chance. Standardized beta coefficients are used in regression analysis to compare the relative influence of independent variables on a dependent variable within a model.
40
Given a correlation coefficient (r) of 0.28, covariance (Cov) of 7.6, and variance of x (Var(x)) of 9, what is the standard deviation of the y series?
Answer:
9.05
The formula for correlation is r = Cov(x,y) / (SD(x) * SD(y)). Given Var(x) = 9, SD(x) = 3. Substituting values: 0.28 = 7.6 / (3 * SD(y)). Thus, 0.84 * SD(y) = 7.6, leading to SD(y) = 7.6 / 0.84, which is approximately 9.0476, rounded to 9.05.