Inflation and Interest Rate Relationship

Business Context

NorthBridge Capital is reviewing whether central bank policy rates move in line with inflation. The research team wants a simple statistical analysis using recent monthly macro data.

Problem Statement

Use the data below to quantify and test the relationship between monthly inflation and the central bank policy interest rate. Treat inflation as the explanatory variable and interest rate as the response variable.

Given Data

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Assume these 12 monthly observations are an independent sample for this exercise. Test significance at $\alpha = 0.05$ .

Requirements

Calculate the sample correlation between inflation and interest rates.
Fit a simple linear regression: interest rate on inflation.
State and test the null hypothesis that the slope is zero.
Compute the t-statistic and p-value for the slope.
Interpret the slope in business terms.
Explain whether the result supports the claim that higher inflation is associated with higher interest rates.

Assumptions

Linear relationship over the observed range
Independent observations for this interview exercise
Residual variance is approximately constant
This analysis measures association, not strict causality

Business Context

NorthBridge Capital is reviewing whether central bank policy rates move in line with inflation. The research team wants a simple statistical analysis using recent monthly macro data.

Problem Statement

Given Data

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Assume these 12 monthly observations are an independent sample for this exercise. Test significance at $\alpha = 0.05$ .

Requirements

Calculate the sample correlation between inflation and interest rates.
Fit a simple linear regression: interest rate on inflation.
State and test the null hypothesis that the slope is zero.
Compute the t-statistic and p-value for the slope.
Interpret the slope in business terms.
Explain whether the result supports the claim that higher inflation is associated with higher interest rates.

Assumptions

Linear relationship over the observed range
Independent observations for this interview exercise
Residual variance is approximately constant
This analysis measures association, not strict causality

Business Context

NorthBridge Capital is reviewing whether central bank policy rates move in line with inflation. The research team wants a simple statistical analysis using recent monthly macro data.

Problem Statement

Given Data

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Assume these 12 monthly observations are an independent sample for this exercise. Test significance at $\alpha = 0.05$ .

Requirements

Calculate the sample correlation between inflation and interest rates.
Fit a simple linear regression: interest rate on inflation.
State and test the null hypothesis that the slope is zero.
Compute the t-statistic and p-value for the slope.
Interpret the slope in business terms.
Explain whether the result supports the claim that higher inflation is associated with higher interest rates.

Assumptions

Linear relationship over the observed range
Independent observations for this interview exercise
Residual variance is approximately constant
This analysis measures association, not strict causality

Business Context

NorthBridge Capital is reviewing whether central bank policy rates move in line with inflation. The research team wants a simple statistical analysis using recent monthly macro data.

Problem Statement

Given Data

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Assume these 12 monthly observations are an independent sample for this exercise. Test significance at $\alpha = 0.05$ .

Requirements

Calculate the sample correlation between inflation and interest rates.
Fit a simple linear regression: interest rate on inflation.
State and test the null hypothesis that the slope is zero.
Compute the t-statistic and p-value for the slope.
Interpret the slope in business terms.
Explain whether the result supports the claim that higher inflation is associated with higher interest rates.

Assumptions

Linear relationship over the observed range
Independent observations for this interview exercise
Residual variance is approximately constant
This analysis measures association, not strict causality

Interview Guides

Business Context

Problem Statement

Given Data

Requirements

Assumptions

Inflation and Interest Rate Relationship

Business Context

Problem Statement

Given Data

Requirements

Assumptions

Your Answer

Inflation and Interest Rate Relationship

Business Context

Problem Statement

Given Data

Requirements

Assumptions

Inflation and Interest Rate Relationship

Business Context

Problem Statement

Given Data

Requirements

Assumptions

Your Answer

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0

Month	Inflation Rate (%)	Policy Interest Rate (%)
1	2.1	2.4
2	2.3	2.5
3	2.5	2.7
4	2.8	2.9
5	3.0	3.1
6	3.4	3.5
7	3.6	3.7
8	3.9	4.0
9	4.1	4.2
10	4.4	4.5
11	4.6	4.8
12	4.9	5.0