1|Page
QMB 3200 Exam| Business Statistics – ANOVA, Chi-
Square, Regression, Forecasting, Hypothesis Testing |
Multiple Choice Q&A | Verified Answers
Exam Structure:
Subject: Business Statistics – ANOVA, Chi-Square, Regression & Forecasting (QMB
3200)
Source: QMB 3200 Exam Test – Verified Answers
Format: Multiple Choice & Open-Ended Q&A
1. What is a chi-squared test used for?
Correct Answer:
1. Testing whether two or more proportions are equal.
2. Determining if data follow a particular pattern (goodness-of-fit test).
3. Testing two categorical variables for independence.
Rationale:
1. The chi-square test is non-parametric (no assumption about population
distribution shape).
2. Goodness-of-fit tests compare observed frequencies to expected
frequencies under a hypothesized distribution.
3. Test of independence assesses association between two categorical
variables in a contingency table.
4. The test statistic follows a chi-square distribution with degrees of
freedom based on the number of categories.
2. What hypothesis does ANOVA test?
Correct Answer: Three or more population means are equal.
Rationale:
1. ANOVA tests H₀: μ₁ = μ₂ = … = μₖ (all population means equal).
2. The alternative hypothesis is that at least one mean is different.
3. ANOVA analyzes variance within and between samples to make inferences
, 2|Page
about means.
4. The F-test is used to determine statistical significance.
3. What are the two broad categories of forecasting techniques?
Correct Answer:
1. Quantitative Forecasting
2. Qualitative Forecasting
Rationale:
1. Quantitative forecasting uses historical data and mathematical models.
2. Qualitative forecasting relies on expert judgment and intuition.
3. Quantitative methods include time series and causal models.
4. Qualitative methods include Delphi method, market research, and executive
opinion.
4. What is forecasting?
Correct Answer: A method to predict or estimate a future event.
Applications include predicting sales, developing budgets, predicting tax
revenues, and predicting economic trends.
Rationale:
1. Forecasting is essential for planning and decision-making.
2. Uses historical data, statistical models, or expert judgment.
3. Forecasts are never perfect; error is expected.
4. Accuracy is measured by MSE, MAD, and MAPE.
5. What is the Mean Squared Error (MSE) formula?
Correct Answer: MSE = (1/n) Σ(eₜ²), where eₜ = forecast error.
Rationale:
1. MSE penalizes large errors more heavily than MAE.
2. Sensitive to outliers.
3. Lower MSE indicates more accurate forecasts.
4. Example calculation shown in the document: MSE = 208.90.
6. What is the Mean Absolute Deviation (MAD) formula?
Correct Answer: MAD = (1/n) Σ|eₜ|.
Rationale:
1. MAD is the average of absolute forecast errors.
2. Less sensitive to outliers than MSE.
, 3|Page
3. Interpreted in same units as original data.
4. Example calculation shown in the document: MAD = 11.85.
7. What is the error term formula?
Correct Answer: Error = Observation – Predicted value (or Moving
Average).
Rationale:
1. Forecast error = Actual – Forecast.
2. Positive error = actual > forecast (underforecast).
3. Negative error = actual < forecast (overforecast).
4. Errors are used to calculate accuracy metrics (MSE, MAD, MAPE).
8. The linear trend model uses what as the predictor variable?
Correct Answer: Time (t).
Rationale:
1. Linear trend model: Tₜ = b₀ + b₁t.
2. Time is the independent variable (x).
3. The dependent variable is the time series value (y).
4. Used to model long-term upward or downward movements.
9. What is trend projection?
Correct Answer: A forecasting technique that projects into the future a
linear regression equation that best fits the data in a time series.
Rationale:
1. Extends the trend line beyond the observed data.
2. Assumes the trend will continue into the future.
3. Can be linear or nonlinear (quadratic, exponential).
4. Forecast for time period t is yₜ = b₀ + b₁t.
10. What is the linear trend model used for?
Correct Answer: To extract long-term upward or downward movements of
the time series.
Rationale:
1. Trend is the long-term direction of the series.
2. Removes short-term fluctuations (seasonal, cyclical, irregular).
3. Helps identify underlying growth or decline.
4. Used as a baseline for more complex forecasting methods.
, 4|Page
11. How does exponential smoothing work?
Correct Answer: Adjusts the previous forecast with a portion of the
previous period’s forecasting error. Needs constant revising.
Rationale:
1. Formula: Fₜ₊₁ = αYₜ + (1-α)Fₜ.
2. α (smoothing constant) ranges from 0 to 1.
3. High α = forecast reacts quickly to changes.
4. Low α = smooth, stable forecast.
12. How does simple exponential smoothing assign weights to
observations?
Correct Answer: Assigns exponentially decreasing weights as the
observations get older.
Rationale:
1. Most recent observation gets the highest weight (α).
2. Older observations get progressively smaller weights.
3. Weights decline geometrically: α, α(1-α), α(1-α)², etc.
4. All past observations are included (infinite memory).
13. What are the shortcomings of the moving average technique?
Correct Answer:
1. Choice of m (number of periods) is arbitrary.
2. Choose m to minimize MSE, MAD, or MAPE.
3. All m observations have the same weight (equal weighting).
Rationale:
1. No objective rule for selecting m.
2. Larger m produces smoother forecasts but less responsiveness.
3. Equal weighting ignores recency (all m observations treated equally).
4. Weighted moving average addresses the equal weighting issue.
14. What is the MAPE formula?
Correct Answer: MAPE = (1/n) Σ(|eₜ/yₜ|) × 100.
Rationale:
1. Mean Absolute Percentage Error expresses error as a percentage.
2. Scale-independent, useful for comparing across different series.
QMB 3200 Exam| Business Statistics – ANOVA, Chi-
Square, Regression, Forecasting, Hypothesis Testing |
Multiple Choice Q&A | Verified Answers
Exam Structure:
Subject: Business Statistics – ANOVA, Chi-Square, Regression & Forecasting (QMB
3200)
Source: QMB 3200 Exam Test – Verified Answers
Format: Multiple Choice & Open-Ended Q&A
1. What is a chi-squared test used for?
Correct Answer:
1. Testing whether two or more proportions are equal.
2. Determining if data follow a particular pattern (goodness-of-fit test).
3. Testing two categorical variables for independence.
Rationale:
1. The chi-square test is non-parametric (no assumption about population
distribution shape).
2. Goodness-of-fit tests compare observed frequencies to expected
frequencies under a hypothesized distribution.
3. Test of independence assesses association between two categorical
variables in a contingency table.
4. The test statistic follows a chi-square distribution with degrees of
freedom based on the number of categories.
2. What hypothesis does ANOVA test?
Correct Answer: Three or more population means are equal.
Rationale:
1. ANOVA tests H₀: μ₁ = μ₂ = … = μₖ (all population means equal).
2. The alternative hypothesis is that at least one mean is different.
3. ANOVA analyzes variance within and between samples to make inferences
, 2|Page
about means.
4. The F-test is used to determine statistical significance.
3. What are the two broad categories of forecasting techniques?
Correct Answer:
1. Quantitative Forecasting
2. Qualitative Forecasting
Rationale:
1. Quantitative forecasting uses historical data and mathematical models.
2. Qualitative forecasting relies on expert judgment and intuition.
3. Quantitative methods include time series and causal models.
4. Qualitative methods include Delphi method, market research, and executive
opinion.
4. What is forecasting?
Correct Answer: A method to predict or estimate a future event.
Applications include predicting sales, developing budgets, predicting tax
revenues, and predicting economic trends.
Rationale:
1. Forecasting is essential for planning and decision-making.
2. Uses historical data, statistical models, or expert judgment.
3. Forecasts are never perfect; error is expected.
4. Accuracy is measured by MSE, MAD, and MAPE.
5. What is the Mean Squared Error (MSE) formula?
Correct Answer: MSE = (1/n) Σ(eₜ²), where eₜ = forecast error.
Rationale:
1. MSE penalizes large errors more heavily than MAE.
2. Sensitive to outliers.
3. Lower MSE indicates more accurate forecasts.
4. Example calculation shown in the document: MSE = 208.90.
6. What is the Mean Absolute Deviation (MAD) formula?
Correct Answer: MAD = (1/n) Σ|eₜ|.
Rationale:
1. MAD is the average of absolute forecast errors.
2. Less sensitive to outliers than MSE.
, 3|Page
3. Interpreted in same units as original data.
4. Example calculation shown in the document: MAD = 11.85.
7. What is the error term formula?
Correct Answer: Error = Observation – Predicted value (or Moving
Average).
Rationale:
1. Forecast error = Actual – Forecast.
2. Positive error = actual > forecast (underforecast).
3. Negative error = actual < forecast (overforecast).
4. Errors are used to calculate accuracy metrics (MSE, MAD, MAPE).
8. The linear trend model uses what as the predictor variable?
Correct Answer: Time (t).
Rationale:
1. Linear trend model: Tₜ = b₀ + b₁t.
2. Time is the independent variable (x).
3. The dependent variable is the time series value (y).
4. Used to model long-term upward or downward movements.
9. What is trend projection?
Correct Answer: A forecasting technique that projects into the future a
linear regression equation that best fits the data in a time series.
Rationale:
1. Extends the trend line beyond the observed data.
2. Assumes the trend will continue into the future.
3. Can be linear or nonlinear (quadratic, exponential).
4. Forecast for time period t is yₜ = b₀ + b₁t.
10. What is the linear trend model used for?
Correct Answer: To extract long-term upward or downward movements of
the time series.
Rationale:
1. Trend is the long-term direction of the series.
2. Removes short-term fluctuations (seasonal, cyclical, irregular).
3. Helps identify underlying growth or decline.
4. Used as a baseline for more complex forecasting methods.
, 4|Page
11. How does exponential smoothing work?
Correct Answer: Adjusts the previous forecast with a portion of the
previous period’s forecasting error. Needs constant revising.
Rationale:
1. Formula: Fₜ₊₁ = αYₜ + (1-α)Fₜ.
2. α (smoothing constant) ranges from 0 to 1.
3. High α = forecast reacts quickly to changes.
4. Low α = smooth, stable forecast.
12. How does simple exponential smoothing assign weights to
observations?
Correct Answer: Assigns exponentially decreasing weights as the
observations get older.
Rationale:
1. Most recent observation gets the highest weight (α).
2. Older observations get progressively smaller weights.
3. Weights decline geometrically: α, α(1-α), α(1-α)², etc.
4. All past observations are included (infinite memory).
13. What are the shortcomings of the moving average technique?
Correct Answer:
1. Choice of m (number of periods) is arbitrary.
2. Choose m to minimize MSE, MAD, or MAPE.
3. All m observations have the same weight (equal weighting).
Rationale:
1. No objective rule for selecting m.
2. Larger m produces smoother forecasts but less responsiveness.
3. Equal weighting ignores recency (all m observations treated equally).
4. Weighted moving average addresses the equal weighting issue.
14. What is the MAPE formula?
Correct Answer: MAPE = (1/n) Σ(|eₜ/yₜ|) × 100.
Rationale:
1. Mean Absolute Percentage Error expresses error as a percentage.
2. Scale-independent, useful for comparing across different series.
