Step 1: Concept Clarification:
The problem asks for the regression coefficient of Mumbai prices (Y) predicted by Kolkata prices (X), denoted as \(b_{YX}\). Mumbai is the dependent variable (Y), and Kolkata is the independent variable (X).
Step 2: Formula:
The regression coefficient \(b_{YX}\) is calculated as:
\[ b_{YX} = r \frac{\sigma_Y}{\sigma_X} \]
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: Calculation:
From the data:
- \(\sigma_Y\) (Mumbai) = 4
- \(\sigma_X\) (Kolkata) = 5
- \(r = 0.6\)
Substituting these values:
\[ b_{YX} = 0.6 \times \frac{4}{5} \]
\[ b_{YX} = 0.6 \times 0.8 \]
\[ b_{YX} = 0.48 \]
The average prices and sample size are irrelevant to this calculation.
Step 4: Answer:
The regression coefficient of Mumbai prices over Kolkata prices is 0.48.