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UCF QMB 3200 Exam 3 | Business Statistics –
Regression & Time Series | Multiple Choice &
Open-Ended Q&A | Verified Answers
Exam Structure:
Subject: Business Statistics – Regression & Time Series (QMB 3200)
Source: UCF QMB 3200 – Exam 3 (Verified Answers)
Format: Multiple Choice & Open-Ended Q&A
1. What is the difference between the observed value of the dependent
variable and the value predicted using the estimated regression
equation called?
Correct Answer: Residual
Rationale:
1. Residual = actual y – predicted y.
2. Residuals measure the error in prediction for each observation.
3. The sum of residuals is zero in ordinary least squares regression.
4. Residual plots are used to check regression assumptions.
2. Influential observations always:
Correct Answer: Increase the value of the correlation.
Rationale:
1. Influential observations have a strong effect on regression results (slope,
intercept, R²).
2. They often increase the correlation coefficient (r) by pulling the regression
line toward them.
3. Removing an influential observation can dramatically change model
estimates.
4. Detected using Cook’s distance or leverage values.
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3. A graph of standardized residuals plotted against normal scores to
determine if the error term has a normal probability distribution is
called a:
Correct Answer: Normal probability plot (Q-Q plot).
Rationale:
1. Normal probability plot compares residuals to theoretical normal
quantiles.
2. If points fall roughly on a straight line, normality assumption is reasonable.
3. Systematic deviations (S-curve, bow-shape) indicate non-normality.
4. Used in regression diagnostics.
4. The tests of significance in regression analysis assume the
relationship between x and y is:
Correct Answer: Linear
Rationale:
1. Simple linear regression assumes a straight-line relationship.
2. Non-linear patterns require transformation or non-linear models.
3. Residual plots can detect non-linearity (curved pattern).
4. Violation of linearity reduces model validity.
5. Suppose a residual plot of x versus residuals shows nonconstant
variance. As x increases, residuals increase. This means:
Correct Answer: As the values of x get larger, the ability to predict y
becomes less accurate.
Rationale:
1. Nonconstant variance = heteroscedasticity.
2. Increasing spread indicates prediction is less precise at higher x values.
3. Violates assumption of constant variance (homoscedasticity).
4. Remedies: weighted least squares or transformation of y (log, square root).
6. In a regression analysis, an outlier will always:
Correct Answer: Increase the value of the correlation.
Rationale:
1. Outliers pull the correlation coefficient toward them.
2. Can increase or decrease r depending on position, but often increases
magnitude.
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3. Outliers can distort the true relationship between variables.
4. Scatter plots and residual analysis help identify outliers.
7. Regression analysis can be interpreted as a procedure for
establishing a cause-and-effect relationship between variables.
Correct Answer: False
Rationale:
1. Regression shows association, not causation.
2. Confounding variables may explain observed relationship.
3. Causation requires controlled experiments or specific causal inference
methods.
4. “Correlation does not imply causation” applies to regression.
8. An F test, based on the F probability distribution, can be used to test
for:
Correct Answer: Significance in regression (overall significance).
Rationale:
1. F test in regression tests H₀: all slopes = 0 vs H₁: at least one slope ≠ 0.
2. F = MSR / MSE.
3. Significant F indicates model explains significant variance in y.
4. Used in both simple and multiple regression.
9. The tests of significance in regression analysis assume that the
values of the error term ε are:
Correct Answer: Independent
Rationale:
1. Independence means residuals are not correlated with each other.
2. Violation occurs in time series (autocorrelation) or clustered data.
3. Durbin-Watson test detects autocorrelation.
4. Independence is critical for valid standard errors and p-values.
10. When constructing a confidence or prediction interval for two
quantitative variables, what distribution do these intervals follow?
Correct Answer: t distribution
Rationale:
1. Population standard deviation of error (σ) is unknown, estimated by s
(standard error of estimate).
UCF QMB 3200 Exam 3 | Business Statistics –
Regression & Time Series | Multiple Choice &
Open-Ended Q&A | Verified Answers
Exam Structure:
Subject: Business Statistics – Regression & Time Series (QMB 3200)
Source: UCF QMB 3200 – Exam 3 (Verified Answers)
Format: Multiple Choice & Open-Ended Q&A
1. What is the difference between the observed value of the dependent
variable and the value predicted using the estimated regression
equation called?
Correct Answer: Residual
Rationale:
1. Residual = actual y – predicted y.
2. Residuals measure the error in prediction for each observation.
3. The sum of residuals is zero in ordinary least squares regression.
4. Residual plots are used to check regression assumptions.
2. Influential observations always:
Correct Answer: Increase the value of the correlation.
Rationale:
1. Influential observations have a strong effect on regression results (slope,
intercept, R²).
2. They often increase the correlation coefficient (r) by pulling the regression
line toward them.
3. Removing an influential observation can dramatically change model
estimates.
4. Detected using Cook’s distance or leverage values.
, 2|Page
3. A graph of standardized residuals plotted against normal scores to
determine if the error term has a normal probability distribution is
called a:
Correct Answer: Normal probability plot (Q-Q plot).
Rationale:
1. Normal probability plot compares residuals to theoretical normal
quantiles.
2. If points fall roughly on a straight line, normality assumption is reasonable.
3. Systematic deviations (S-curve, bow-shape) indicate non-normality.
4. Used in regression diagnostics.
4. The tests of significance in regression analysis assume the
relationship between x and y is:
Correct Answer: Linear
Rationale:
1. Simple linear regression assumes a straight-line relationship.
2. Non-linear patterns require transformation or non-linear models.
3. Residual plots can detect non-linearity (curved pattern).
4. Violation of linearity reduces model validity.
5. Suppose a residual plot of x versus residuals shows nonconstant
variance. As x increases, residuals increase. This means:
Correct Answer: As the values of x get larger, the ability to predict y
becomes less accurate.
Rationale:
1. Nonconstant variance = heteroscedasticity.
2. Increasing spread indicates prediction is less precise at higher x values.
3. Violates assumption of constant variance (homoscedasticity).
4. Remedies: weighted least squares or transformation of y (log, square root).
6. In a regression analysis, an outlier will always:
Correct Answer: Increase the value of the correlation.
Rationale:
1. Outliers pull the correlation coefficient toward them.
2. Can increase or decrease r depending on position, but often increases
magnitude.
, 3|Page
3. Outliers can distort the true relationship between variables.
4. Scatter plots and residual analysis help identify outliers.
7. Regression analysis can be interpreted as a procedure for
establishing a cause-and-effect relationship between variables.
Correct Answer: False
Rationale:
1. Regression shows association, not causation.
2. Confounding variables may explain observed relationship.
3. Causation requires controlled experiments or specific causal inference
methods.
4. “Correlation does not imply causation” applies to regression.
8. An F test, based on the F probability distribution, can be used to test
for:
Correct Answer: Significance in regression (overall significance).
Rationale:
1. F test in regression tests H₀: all slopes = 0 vs H₁: at least one slope ≠ 0.
2. F = MSR / MSE.
3. Significant F indicates model explains significant variance in y.
4. Used in both simple and multiple regression.
9. The tests of significance in regression analysis assume that the
values of the error term ε are:
Correct Answer: Independent
Rationale:
1. Independence means residuals are not correlated with each other.
2. Violation occurs in time series (autocorrelation) or clustered data.
3. Durbin-Watson test detects autocorrelation.
4. Independence is critical for valid standard errors and p-values.
10. When constructing a confidence or prediction interval for two
quantitative variables, what distribution do these intervals follow?
Correct Answer: t distribution
Rationale:
1. Population standard deviation of error (σ) is unknown, estimated by s
(standard error of estimate).
