Question

The regression coefficient of Mumbai prices over Kolkata prices from the following table, is: 

 

	Mumbai (₹)	Kolkata (₹)
Average price (per 5 kg)	120	130
S.D.	4	5
Correlation coefficient	0.6
N (Sample size)	100

• A. 0.48
• B. 0.40
• C. 0.53
• D. 0.60

Hint:

Pay close attention to the wording "Y over X" or "Y on X". The variable mentioned first is the dependent variable (Y), and the one mentioned second is the independent variable (X). This determines which standard deviation goes in the numerator of the formula.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The question asks for the "regression coefficient of Mumbai prices over Kolkata prices". This phrasing means we are predicting Mumbai prices based on Kolkata prices. Therefore, Mumbai price is the dependent variable (Y) and Kolkata price is the independent variable (X). We need to find the regression coefficient \(b_{YX}\).

Step 2: Key Formula or Approach:
The formula for the regression coefficient of Y on X is: \[ b_{YX} = r \frac{\sigma_Y}{\sigma_X} \] where \(r\) is the correlation coefficient, \(\sigma_Y\) is the standard deviation of Y, and \(\sigma_X\) is the standard deviation of X.

Step 3: Detailed Explanation:
From the table, we identify the necessary values: - Dependent variable Y: Mumbai prices. So, \(\sigma_Y = 4\). - Independent variable X: Kolkata prices. So, \(\sigma_X = 5\). - Correlation coefficient, \(r = 0.6\). Now, substitute these values into the formula: \[ b_{YX} = 0.6 \times \frac{4}{5} \] \[ b_{YX} = 0.6 \times 0.8 \] \[ b_{YX} = 0.48 \] The average prices and the sample size are extra information not needed for this specific calculation.
Step 4: Final Answer:
The regression coefficient of Mumbai prices over Kolkata prices is 0.48.