Top 100 Mathematics & Statistics Interview Questions for Business Analysts (12 LPA Ready) Part 2: Hypothesis Testing, Regression, and Forecasting

Introduction

Once you understand descriptive statistics and probability, the next step in your analytical journey is learning how to test assumptions and model business relationships. That’s where hypothesis testing, regression, and forecasting come in.

In Part 2 of our series, we dive deep into the methods that Business Analysts use to validate ideas, uncover patterns, and make predictions. You’ll learn about null and alternative hypotheses, p-values, t-tests, ANOVA, regression analysis, and forecasting models.

These topics are among the most frequently asked in Business Analyst interviews — especially for roles offering salaries up to ₹12 LPA. Each answer is written in clear, conversational language, with real-world examples that connect statistics to everyday business decisions.

By mastering these topics, you’ll gain the confidence to discuss models, explain results, and demonstrate how data can drive meaningful outcomes for your organization.

SECTION 3: INFERENTIAL STATISTICS & HYPOTHESIS TESTING

36. What is sampling bias and why is it dangerous in business analysis?

Sampling bias occurs when the sample doesn’t represent the whole population. For example, if you only survey customers in metro cities but not in small towns, your insights won’t reflect overall behavior.It’s dangerous because biased samples can lead to wrong business conclusions — like assuming high satisfaction while missing complaints from smaller markets.Analysts prevent this by using random sampling and ensuring diversity in survey design.

37. What is hypothesis testing in simple terms?

Hypothesis testing is a method used to check whether a claim or assumption about data is true.You start with a null hypothesis (H₀) — a statement of “no change” (e.g., new ad campaign doesn’t affect sales).Then you test it using data. If evidence is strong (low p-value), you reject H₀ in favor of the alternative hypothesis (H₁) — meaning the campaign did affect sales.Business Analysts use it to validate strategies before full rollout.

38. What is a null and alternative hypothesis? Give an example.

The null hypothesis (H₀) assumes no effect or relationship. The alternative hypothesis (H₁) assumes an effect or difference exists.For instance:

• H₀: “Average sales before and after training are equal.”

• H₁: “Average sales after training are higher.”

  
  

  Analysts test H₀ using sample data to decide whether the observed difference is due to real change or just chance.

  
  

39. What is a p-value and how do you interpret it?

A p-value shows the probability of observing results as extreme as the sample data if the null hypothesis were true.A smaller p-value (≤ 0.05) means stronger evidence against H₀.For example, if you test whether a new pricing strategy increases sales and p = 0.02, there’s only a 2% chance this improvement happened randomly — meaning it’s statistically significant.

40. What are Type I and Type II errors?

A Type I error happens when you wrongly reject a true null hypothesis (false positive), and a Type II error happens when you fail to reject a false null (false negative).Example:

• Type I: Concluding a new ad works when it doesn’t.

• Type II: Missing a genuinely effective ad.

  
  

  Business Analysts balance both by setting correct confidence levels (usually 95%) and sample sizes.

  
  

41. What is statistical significance and practical significance?

Statistical significance means results are unlikely due to chance (p < 0.05). Practical significance means the result actually matters to the business.For example, a new campaign increases sales by ₹100 with p = 0.001 — statistically significant but not practical.Analysts must evaluate both — focusing not just on mathematical proof but also business impact.

42. What is a confidence interval and how do you interpret it?

A confidence interval (CI) gives a range of likely values for a population parameter.For example, if the average customer spend is ₹1,000 with a 95% CI of ₹950–₹1,050, it means we’re 95% confident the true mean lies in that range.It’s widely used to estimate metrics like average satisfaction or conversion rate without measuring the entire population.

43. What is the difference between a z-test and t-test?

Both compare means, but:

• Z-test is used when the population standard deviation is known or sample size is large (n > 30).

• T-test is used when variance is unknown or sample is small.

  
  

  Example: To compare average customer spending in two small store branches, a t-test is appropriate.

  
  

44. What are one-sample, two-sample, and paired t-tests?

• One-sample t-test: compares sample mean with a fixed value (e.g., average sales vs target).

• Two-sample t-test: compares means of two independent groups (e.g., two branches).

• Paired t-test: compares means of related samples (e.g., sales before and after training).

  
  

  These help analysts check if observed differences are statistically meaningful.

  
  

45. What is ANOVA and when is it used?

ANOVA (Analysis of Variance) compares the means of three or more groups to see if at least one differs significantly.Example: A BA may compare customer satisfaction across three regions — North, South, and West.If the p-value is below 0.05, it means at least one region’s satisfaction score differs, prompting deeper investigation.

46. What is the Chi-square test?

A Chi-square test examines relationships between categorical variables.Example: An analyst might test if “gender” and “loan approval” are related.If the test shows significance, gender likely influences approval rates.It’s a common tool for survey data, customer segmentation, and fraud detection where variables are not numerical.

47. What is sample size, and why is it important in hypothesis testing?

Sample size affects accuracy. A larger sample gives more reliable results by reducing variability and increasing test power.For instance, testing a new product feature on 1,000 users gives stronger evidence than 50 users.Too small a sample may miss real effects (Type II error), while too large may make even tiny differences look “significant.”

48. What is the power of a test?

The power of a test is the probability of correctly rejecting a false null hypothesis.A higher power (usually >80%) means you’re more likely to detect real effects.For example, in A/B testing, low power may cause you to overlook a beneficial change.Power depends on effect size, significance level, and sample size — all must be balanced for strong conclusions.

49. What is Bonferroni correction and when is it used?

When multiple statistical tests are performed simultaneously, the chance of false positives increases.The Bonferroni correction divides the significance level (e.g., 0.05) by the number of tests, making the criteria stricter.For example, testing 5 campaigns at once would set α = 0.05/5 = 0.01 per test.Business Analysts use this when evaluating multiple hypotheses from the same dataset to maintain integrity.

SECTION 4: REGRESSION & RELATIONSHIP ANALYSIS

50. What is simple linear regression and how is it useful for business analysts?

Simple linear regression models the relationship between one independent variable (X) and a dependent variable (Y):

For example, predicting sales (Y) based on marketing spend (X).It helps analysts quantify relationships — for every ₹1,000 spent on marketing, how much additional sales can be expected? This allows for data-driven budgeting and forecasting.

51. What is multiple regression?

Multiple regression includes more than one predictor variable to explain or predict a target variable.For example, predicting monthly revenue using “ad spend,” “price,” and “discount rate.”Each coefficient shows how that variable influences the outcome while holding others constant.Business Analysts use multiple regression to find which factors most strongly drive business performance.

52. What is R-squared and adjusted R-squared?

R² indicates how much variation in the dependent variable is explained by the model (ranges 0–1).Adjusted R² penalizes adding unnecessary predictors.For example, if R² = 0.8, it means 80% of sales variation is explained by chosen variables.Adjusted R² is preferred when comparing models with different numbers of predictors — ensuring performance isn’t inflated by overfitting.

53. What is multicollinearity and why is it a problem?

Multicollinearity happens when predictor variables are highly correlated (e.g., “marketing spend” and “ad clicks”).It makes it hard to know which variable truly affects the outcome, and leads to unstable coefficient estimates.Business Analysts detect it using VIF (Variance Inflation Factor) — a VIF > 5 indicates a problem.To fix it, analysts can remove or combine correlated variables.

54. What is heteroscedasticity?

In regression, heteroscedasticity means residuals (errors) have unequal variance — common in income or price data.This violates one assumption of linear regression and can make standard errors unreliable.For example, prediction errors might be larger for higher-income groups.Analysts use transformations (like log) or robust standard errors to handle it.

55. What is autocorrelation and where does it occur?

Autocorrelation occurs when residuals are correlated over time — typical in time-series data.Example: If this month’s sales are closely tied to last month’s, residuals won’t be independent.It indicates a time pattern the model didn’t capture.Analysts detect it using the Durbin–Watson test and address it using time-series models (like ARIMA).

56. What are dummy variables and how are they used?

Dummy variables represent categorical data numerically (0/1) for regression.Example: “Region = North” can be 1 for North, 0 otherwise.This allows inclusion of non-numeric variables like gender, region, or plan type in models.Analysts must avoid the dummy variable trap by excluding one category as a reference.

57. What are interaction terms in regression?

Interaction terms show when one variable’s effect depends on another.For example, the effect of “Discount” on sales may differ by “Region.”Adding a term “Discount × Region” helps capture that difference.Business Analysts use interaction terms to uncover such combined effects in campaigns or pricing analysis.

58. What is logistic regression and when is it used?

Logistic regression is used when the outcome is binary (yes/no, churn/no churn).It predicts the probability of an event using a logistic function.Example: predicting whether a customer will buy after a campaign.Instead of predicting sales value, it predicts likelihood — perfect for classification problems like churn analysis, fraud detection, or lead conversion.

59. What is correlation vs regression?

Correlation measures the strength and direction of a relationship, while regression quantifies and predicts it.For example, correlation shows sales and ads are related (r = 0.8), while regression predicts: “Each ₹1,000 in ad spend adds ₹5,000 in sales.”Correlation is symmetric; regression is directional.

60. What is the difference between linear and nonlinear relationships?

Linear relationships change at a constant rate (straight-line), while nonlinear ones curve.Example: advertising spend may boost sales linearly up to ₹1L, then flatten — showing diminishing returns.Business Analysts recognize such patterns to avoid overinvestment and model realistic business growth.

61. What is multivariate regression vs multiple regression? (optional)

Multiple regression: one dependent variable, many predictors.Multivariate regression: multiple dependent variables predicted simultaneously.Example: predicting both “sales” and “customer satisfaction” using common inputs.Less common in BA interviews but useful in advanced analytics.

62. What is residual analysis and why is it important?

Residuals are differences between predicted and actual values.Plotting them helps analysts check model fit — random scatter means good model; patterns mean missing relationships.For example, if errors increase with predicted sales, heteroscedasticity exists.Residual analysis ensures model reliability before using it for business forecasting.

63. What is the bias–variance tradeoff?

A high-bias model is too simple (underfits), while a high-variance model is too complex (overfits).For example, a model predicting sales using just one feature may miss patterns (bias), while one with 20 features may capture noise (variance).Analysts balance both for the best predictive performance using validation techniques.

64. What is cross-validation and why is it used?

Cross-validation tests how well a model performs on unseen data.Example: splitting data into 5 parts, training on 4, testing on 1, and repeating (k-fold).It helps ensure models generalize beyond training data — critical for making accurate forecasts.

65. What is overfitting and underfitting in regression models?

Overfitting occurs when a model fits training data too well, including noise — performs poorly on new data.Underfitting happens when a model is too simple and misses real trends.Business Analysts use validation data and adjusted R² to detect these issues.

66. What is regularization (ridge, lasso)?

Regularization penalizes large coefficients to prevent overfitting.Ridge (L2) shrinks coefficients smoothly; Lasso (L1) can reduce some to zero.Used in automated feature selection and predictive modeling.

67. What is the difference between time series and cross-sectional data?

Time series: observations over time (monthly sales).Cross-sectional: observations at one point in time (sales across regions).Understanding which type you’re analyzing helps choose correct models (e.g., ARIMA for time series, regression for cross-sectional).

68. What is moving average forecasting?

It smooths out short-term fluctuations by averaging data over a fixed period.

Example: a 3-month moving average helps identify trends in monthly sales, ignoring random spikes.Useful for demand forecasting and inventory planning.

69. What is exponential smoothing?

It gives more weight to recent data while still considering past values.Example: predicting next month’s demand where recent sales matter more.Business Analysts use it for sales, traffic, or KPI trend forecasting due to simplicity and adaptability.

70. What are MAE, MSE, and RMSE?

These are model error metrics:

• MAE: average absolute difference

• MSE: average squared difference

• RMSE: square root of MSE (same units as target)

  
  

  Example: MAE = ₹1,000 means your forecast is off by ₹1,000 on average. RMSE penalizes large errors more, making it good for precision-focused tasks.

  
  

Part 3: Forecasting, Business Applications & Case-Based Math for Analysts (Click Here)