Business Context
At FinVista Research, an analyst is reviewing whether central bank policy rates tend to move with inflation. You are given a small monthly sample and asked to quantify the relationship statistically rather than answer qualitatively.
Problem Statement
Use the data below to evaluate whether inflation is positively associated with the central bank policy interest rate, and estimate how much the rate changes for a 1 percentage point increase in inflation.
Given Data
Monthly observations for the last 8 months:
| Month | Inflation (%) | Policy Rate (%) |
|---|
| 1 | 2.1 | 2.4 |
| 2 | 2.4 | 2.6 |
| 3 | 2.8 | 2.9 |
| 4 | 3.0 | 3.1 |
| 5 | 3.3 | 3.5 |
| 6 | 3.7 | 3.8 |
| 7 | 4.0 | 4.2 |
| 8 | 4.4 | 4.5 |
Test at significance level α=0.05.
Requirements
- Compute the sample correlation between inflation and interest rates.
- Fit a simple linear regression with interest rate as the dependent variable and inflation as the independent variable.
- State the null and alternative hypotheses for the slope.
- Test whether the slope is significantly greater than 0.
- Interpret the slope in business terms.
- Explain what the result says about relationship vs causation.
Assumptions
- Treat the 8 monthly observations as paired measurements.
- Assume a linear relationship over this range.
- Ignore other macroeconomic drivers such as unemployment, growth, and exchange rates.
- Use standard simple linear regression assumptions for inference.
