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
201
Which of the following correlation coefficient (r) values indicates a high degree of correlation?
Answer:
r = 0.9
The correlation coefficient ranges from -1 to +1. A value of 0.9 indicates a very strong positive linear relationship between two variables, which is significantly higher than the other options provided, representing a high degree of correlation.
202
How many variables are involved in a simple regression equation?
Answer:
2
A simple linear regression model examines the relationship between two variables: one independent variable (predictor) and one dependent variable (response). The equation typically takes the form Y = a + bX, where Y is the dependent variable and X is the independent variable. Multiple regression, by contrast, involves more than two variables.
203
What is the standard formula used to calculate the concurrent deviation correlation coefficient?
Answer:
$$ \pm \sqrt { \pm \left( {\frac{{2c - n}}{n}} \right)} $$
The coefficient of concurrent deviations is a simple method to measure the correlation between two series. The formula uses 'c' as the number of concurrent deviations and 'n' as the number of pairs of deviations. The result is expressed as plus or minus the square root of the absolute value of (2c-n)/n, reflecting the direction of the relationship.
204
Given the regression equation 3Y - 5X + 110 = 0, where X is profit and Y is sales, calculate the profit if sales (Y) equal Rs. 4,400.
Answer:
Rs. 26,422
Substitute Y = 4400 into the equation: 3(4400) - 5X + 110 = 0. This simplifies to 13200 - 5X + 110 = 0, which is 13310 = 5X. Solving for X gives 13310 / 5 = 2662. Note: The provided answer 26,422 appears to conflict with the algebraic result.
205
When the dependent variable increases in tandem with the independent variable in a linear regression model, what is the expected range for the correlation coefficient?
Answer:
0 to 1
A positive correlation coefficient indicates that as one variable increases, the other also increases. The range for a positive correlation is between 0 and +1. A value of 0 indicates no linear relationship, while +1 indicates a perfect positive linear relationship. Since the variables move in the same direction, the coefficient must be positive.
206
What does a correlation coefficient of 0 indicate regarding the relationship between two variables?
Answer:
perfect correlation
There is a potential conflict in the provided answer key. Mathematically, a correlation coefficient of 0 indicates no linear correlation. The answer key suggests 'perfect correlation', which typically corresponds to a value of +1 or -1. We retain the provided answer key as per instructions.
207
Which of the following statements regarding correlation and regression is false?
Answer:
Regression co-efficients are independent of both the origin and scale
Regression coefficients are independent of the change of origin but are NOT independent of the change of scale. Therefore, the statement claiming they are independent of both is false.
208
What specific result does the concurrent deviation method of correlation indicate?
Answer:
Direction of co-changes
The concurrent deviation method is a simple, non-parametric approach to correlation. It only considers the signs of the deviations of variables from their respective means. Consequently, it only indicates the direction of the relationship (whether variables move together or in opposite directions) rather than the precise degree or magnitude of the correlation.
209
If the unexplained variation between two variables, X and Y, is 36%, what is the coefficient of correlation?
Answer:
0.80
The coefficient of determination (r²) represents the explained variation. If the unexplained variation is 36%, the explained variation is 100% - 36% = 64% (or 0.64). The coefficient of correlation (r) is the square root of the coefficient of determination. Therefore, r = sqrt(0.64) = 0.80. This indicates a strong positive linear relationship between the two variables.
210
Evaluate the following: Assertion (A) The correlation coefficient 'r' lies between -1 and +1. Reason (R) r = +1 indicates perfect positive correlation, and r = -1 indicates perfect negative correlation.
Answer:
Both (A) and (R) are true
The correlation coefficient is bounded by -1 and +1. A value of +1 signifies a perfect positive linear relationship, while -1 signifies a perfect negative linear relationship. Both the assertion and the reason are statistically accurate descriptions of the Pearson correlation coefficient properties.