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Correlation vs Causation in Marketing Spend

Easy

Statistics & Probability

CorrelationRegressionCausal Inference

Problem

Business Context

StreamCart, a grocery delivery app, noticed that weeks with higher paid marketing spend also had higher order volume. The growth team wants to know whether this relationship proves that increasing ad spend causes more orders.

Problem Statement

You are given 8 weeks of data on marketing spend and total orders. Quantify the linear relationship using correlation, test whether it is statistically different from zero, and explain why a strong correlation does not by itself establish causation.

Given Data

Week	Marketing Spend ($000)	Orders (000)
1	20	100
2	22	104
3	25	108
4	28	115
5	30	120
6	35	130
7	40	145
8	45	150

Assume a significance level of 0.05 for testing whether the population correlation is zero.

Requirements

Calculate the sample Pearson correlation between marketing spend and orders.
Test the null hypothesis that the population correlation is zero.
Compute the corresponding t-statistic and p-value.
State whether the correlation is statistically significant at $\alpha = 0.05$ .
Explain clearly, in business terms, why correlation does not imply causation.
Give at least two plausible confounders or alternative explanations for the observed relationship.

Assumptions

Treat each week as an independent observation.
Use Pearson correlation for a linear relationship.
Assume the test statistic follows a t-distribution with $n-2$ degrees of freedom under the null.

Sample Data

Example 1

Input

{"alpha":0.05,"orders_k":[100,104,108,115,120,130,145,150],"sample_size":8,"marketing_spend_k":[20,22,25,28,30,35,40,45]}

Output(none)

Problem

Business Context

Problem Statement

Given Data

Week	Marketing Spend ($000)	Orders (000)
1	20	100
2	22	104
3	25	108
4	28	115
5	30	120
6	35	130
7	40	145
8	45	150

Assume a significance level of 0.05 for testing whether the population correlation is zero.

Requirements

Calculate the sample Pearson correlation between marketing spend and orders.
Test the null hypothesis that the population correlation is zero.
Compute the corresponding t-statistic and p-value.
State whether the correlation is statistically significant at $\alpha = 0.05$ .
Explain clearly, in business terms, why correlation does not imply causation.
Give at least two plausible confounders or alternative explanations for the observed relationship.

Assumptions

Treat each week as an independent observation.
Use Pearson correlation for a linear relationship.
Assume the test statistic follows a t-distribution with $n-2$ degrees of freedom under the null.

Sample Data

Example 1

Input

{"alpha":0.05,"orders_k":[100,104,108,115,120,130,145,150],"sample_size":8,"marketing_spend_k":[20,22,25,28,30,35,40,45]}

Output(none)

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Correlation vs Causation in Marketing Spend

Easy

Statistics & Probability

CorrelationRegressionCausal Inference

Problem

Business Context

Problem Statement

Given Data

Week	Marketing Spend ($000)	Orders (000)
1	20	100
2	22	104
3	25	108
4	28	115
5	30	120
6	35	130
7	40	145
8	45	150

Assume a significance level of 0.05 for testing whether the population correlation is zero.

Requirements

Calculate the sample Pearson correlation between marketing spend and orders.
Test the null hypothesis that the population correlation is zero.
Compute the corresponding t-statistic and p-value.
State whether the correlation is statistically significant at $\alpha = 0.05$ .
Explain clearly, in business terms, why correlation does not imply causation.
Give at least two plausible confounders or alternative explanations for the observed relationship.

Assumptions

Treat each week as an independent observation.
Use Pearson correlation for a linear relationship.
Assume the test statistic follows a t-distribution with $n-2$ degrees of freedom under the null.

Sample Data

Example 1

Input

{"alpha":0.05,"orders_k":[100,104,108,115,120,130,145,150],"sample_size":8,"marketing_spend_k":[20,22,25,28,30,35,40,45]}

Output(none)

Problem

Business Context

Problem Statement

Given Data

Week	Marketing Spend ($000)	Orders (000)
1	20	100
2	22	104
3	25	108
4	28	115
5	30	120
6	35	130
7	40	145
8	45	150

Assume a significance level of 0.05 for testing whether the population correlation is zero.

Requirements

Calculate the sample Pearson correlation between marketing spend and orders.
Test the null hypothesis that the population correlation is zero.
Compute the corresponding t-statistic and p-value.
State whether the correlation is statistically significant at $\alpha = 0.05$ .
Explain clearly, in business terms, why correlation does not imply causation.
Give at least two plausible confounders or alternative explanations for the observed relationship.

Assumptions

Treat each week as an independent observation.
Use Pearson correlation for a linear relationship.
Assume the test statistic follows a t-distribution with $n-2$ degrees of freedom under the null.

Sample Data

Example 1

Input

{"alpha":0.05,"orders_k":[100,104,108,115,120,130,145,150],"sample_size":8,"marketing_spend_k":[20,22,25,28,30,35,40,45]}

Output(none)

Your answer

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Get structured feedback, scored against a 4-axis rubric. Premium unlocks unlimited.

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