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
191
What is the range of values for Karl Pearson's correlation coefficient?
Answer:
±1
Karl Pearson's correlation coefficient, denoted by 'r', measures the strength and direction of a linear relationship between two variables. Its value always falls within the range of -1 to +1 inclusive. A value of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
192
Which estimated coefficient indicates the degree to which estimated values are influenced by random factors?
Answer:
standard error of estimated coefficient
The standard error of an estimated coefficient measures the precision of the estimate. It quantifies how much the coefficient is expected to fluctuate due to random sampling error. A smaller standard error indicates that the estimate is more precise and less affected by random noise, providing greater confidence in the regression model's ability to predict outcomes accurately.
193
Which level of measurement is generally considered unsuitable for calculating the Karl Pearson correlation coefficient?
Answer:
Nominal
Karl Pearson's correlation coefficient requires quantitative data measured on an interval or ratio scale because it relies on the mean and standard deviation. Nominal data consists of categories without numerical order or magnitude, making it impossible to calculate the necessary arithmetic means or variances required for the Pearson formula.
194
How would you interpret a correlation coefficient of 0.74 between two variables X and Y?
Answer:
Middle level of positive correlation
A correlation coefficient of 0.74 indicates a positive relationship. In many statistical contexts, values between 0.5 and 0.75 are considered to represent a moderate or 'middle' level of correlation, whereas values closer to 1.0 are considered high. Thus, 0.74 is categorized as a moderate or middle-level positive correlation.
195
If one regression coefficient is positive, what is the sign of the other regression coefficient?
Answer:
Positive
The two regression coefficients (bxy and byx) must have the same sign. This is because they are both related to the correlation coefficient (r) by the formula r = sqrt(bxy * byx). Since the square root of a product must be real, the product of the coefficients must be positive, implying they share the same sign.
196
How does the magnitude of the standard error of estimate affect the dispersion of observed data points around the regression line?
Answer:
greater
The standard error of estimate measures the accuracy of predictions made by a regression model. A larger standard error indicates that the observed data points are more widely spread out or dispersed from the regression line, suggesting a weaker relationship between the variables and lower predictive precision compared to a model with a smaller standard error.
197
If both regression coefficients, bxy and byx, are negative, what is the sign of the correlation coefficient (r)?
Answer:
Negative
The correlation coefficient r is the geometric mean of the two regression coefficients bxy and byx. Mathematically, r = ±√(bxy * byx). Since both regression coefficients share the same sign, the correlation coefficient must carry that same negative sign to maintain the relationship between the variables.
198
If the regression coefficient between two variables is zero, what is the nature of the relationship between them?
Answer:
Independent
A regression coefficient of zero indicates that there is no linear relationship between the independent and dependent variables. Consequently, the variables are considered independent, as changes in one do not predict changes in the other.
199
When calculating a regression equation between two variables, which of the following statements regarding the variables is correct?
Answer:
Y must be the dependent variable
In standard linear regression analysis, the regression equation is expressed as Y = a + bX. In this model, Y is defined as the dependent variable (the outcome being predicted), while X is the independent variable (the predictor).
200
If the coefficient of determination (r²) is 0.81, what is the value of the correlation coefficient (r)?
Answer:
could be either +0.9 or -0.9
The coefficient of determination is the square of the correlation coefficient (r²). Since r² = 0.81, taking the square root gives r = ±0.9. Therefore, the correlation coefficient can be either positive or negative depending on the direction of the relationship between the variables.