QCM : Regression Analysis Fundamentals — 20 questions

Questions et réponses du QCM

1. What is the main goal of the unit's overall approach to statistical analysis?

To train students in advanced data visualization software
To focus only on nonparametric tests for ordinal data
To teach experimental design for establishing causal relationships
To provide a framework for statistical analyses using the Generalized Linear Model

To provide a framework for statistical analyses using the Generalized Linear Model

Explication

The unit’s stated main goal is to provide a framework for statistical analyses using the Generalized Linear Model (GLM). The other options describe useful skills, but they are not the unit’s central aim.

2. Which statement best describes how the unit's lectures are delivered and accessed later?

They meet only online, with no live component or recordings
They run live on Fridays and are later available as Echo360 recordings
They occur only in tutorials, with lecture notes posted afterward
They are pre-recorded and released without any scheduled class time

They run live on Fridays and are later available as Echo360 recordings

Explication

The unit runs live lectures on Fridays and they are live-streamed, then available later through Echo360. This makes the second option correct.

3. Which assessment is a compulsory on-campus task worth 20% of the final unit mark?

The weekly exercise set
The final exam
The data-analysis task
The practical project

The data-analysis task

Explication

The data-analysis task is the compulsory on-campus e-task worth 20% of the final mark. The practical project and final exam have different weights.

4. What is true about the weekly exercises in this unit?

They are iLearn tasks based on previous material or earlier revision
They count as the final exam preparation notes
They are submitted through TurnItIn as part of the practical project
They are based on the current week's lecture and must be finished during class

They are iLearn tasks based on previous material or earlier revision

Explication

Weekly exercises are linked to prior lecture material or earlier revision, not the current week. They are completed on iLearn.

5. In simple regression, what does the symbol y represent?

The amount of variation explained by the fitted line
The residual difference between observed and predicted values
A numeric outcome predicted from one or more predictors
The correlation between two predictors

A numeric outcome predicted from one or more predictors

Explication

Regression predicts a numeric outcome y from one or more numeric predictors x. Residuals and explained variation are related quantities, but not what y means.

6. What does the residual in regression represent?

The overall mean of the outcome variable
The slope of the fitted regression line
The total variation in the outcome explained by the model
The difference between an observed value and its predicted value

The difference between an observed value and its predicted value

Explication

The residual is observed y minus predicted y-hat, capturing unexplained variation. It is not the slope or the total explained variation.

7. What fitted prediction equation was obtained for the simple regression of PSYU3349 SNG on TUTORIALS?

y = 0.55 + 73.27x
y = 0.73 + 73.27x
y = 73.266 - 0.545x
y = 73.27 + 0.55x

y = 73.27 + 0.55x

Explication

The fitted line reported for the example is y = 73.27 + 0.55x. The intercept is about 73.266 and the slope is about 0.545.

8. How should the slope in the example regression be interpreted?

The model explains 0.55 percent of the variance in the outcome
The intercept changes by 0.55 when x equals zero
The outcome decreases by 73.27 points for each tutorial session
Each extra tutorial session is associated with a 0.55-point increase in PSYU3349 SNG

Each extra tutorial session is associated with a 0.55-point increase in PSYU3349 SNG

Explication

The slope indicates the fitted mean change in y for a 1-unit increase in x, which here is a 0.55-point increase per additional tutorial session. The intercept is the predicted value when x = 0.

9. What is the goal of model fit in simple linear regression?

To ensure the residuals are exactly zero for every case
To replace prediction intervals with exact outcome values
To maximize the number of predictors in the model
To make the variation around the regression line smaller than the variation around the overall mean

To make the variation around the regression line smaller than the variation around the overall mean

Explication

Model fit aims to reduce the spread of y around the regression line compared with spread around the overall mean. It does not make residuals zero in real data.

10. In the tutorial example at x = 3, which prediction interval is reported for y?

[56.76, 93.08]
[74.92, 83.08]
[60.00, 90.00]
[65.84, 84.00]

[56.76, 93.08]

Explication

Using the conditional mean of 74.92 and SD of 9.08 gives an approximate 95% interval of mean ± 2 SD, or [56.76, 93.08]. The other intervals do not match the stated calculation.

11. In simple linear regression, which assumption requires the mean of the outcome to change approximately in a straight-line pattern across the observed range of the predictor?

Linearity of the relationship
Normality of residuals
Independence of observations
Constant sample size across predictors

Linearity of the relationship

Explication

Linearity means the expected value of y changes approximately linearly with x across the observed range. The other options refer to different regression assumptions.

12. What pattern on a residual-versus-fitted plot most strongly suggests heteroscedasticity in a simple regression model?

Residuals all lying exactly on the fitted line
A straight-line trend in the raw outcome values
Residual spread increasing or decreasing in a fanning shape
Residuals forming a random horizontal band with equal spread

Residual spread increasing or decreasing in a fanning shape

Explication

Heteroscedasticity is indicated when the conditional variance changes across fitted values, often appearing as a fan shape. A random band with equal spread is more consistent with homoscedasticity.

13. What is the recommended first step in the multiple regression workflow before examining relationships among variables?

Summarize each variable separately with univariate descriptions
Fit the final reduced model immediately
Interpret coefficients while holding all predictors constant
Drop any predictor with a correlation below 0.70

Summarize each variable separately with univariate descriptions

Explication

The workflow begins with univariate data description so each variable can be checked on its own before bivariate or multivariate analysis. Model fitting comes later.

14. Which sample-size guideline is suggested for planning a multiple regression model with p predictors?

n should be greater than 5p, preferably greater than 10p
n should equal 20 regardless of p
n should be exactly equal to p
n should be less than 5p to avoid overfitting

n should be greater than 5p, preferably greater than 10p

Explication

The guideline given is at least n > 5p, with n > 10p preferred. This helps ensure the model is adequately sized for the number of predictors.

15. When writing univariate descriptives for a histogram, which set of features should be commented on for each variable?

Intercept, slope, and prediction error
Central tendency, variability, skewness, kurtosis, and modality
Mean, median, and regression slope
Correlation, collinearity, and residual variance

Central tendency, variability, skewness, kurtosis, and modality

Explication

Univariate description uses a five-point structure: central tendency, variability, skewness, kurtosis, and modality. The other options mix in regression or correlation concepts.

16. In a bivariate graphical screening step, what should be plotted to inspect how variables relate before fitting the model?

Residuals against the sample size only
Only the dependent variable over time
The dependent variable against each independent variable and the independent variables against each other
The intercept against the slope for each predictor

The dependent variable against each independent variable and the independent variables against each other

Explication

Bivariate graphical screening includes DV-versus-IV plots and IV-versus-IV plots to check relationships and possible outliers. This helps before moving to model fitting.

17. What does a tolerance value below 0.1 suggest about a predictor in multiple regression?

The predictor has no relationship with the outcome
The predictor is hard to distinguish from the other predictors
The predictor explains nearly all outcome variance by itself
The predictor must be removed from every model

The predictor is hard to distinguish from the other predictors

Explication

Tolerance below 0.1 indicates very little variance in that predictor is left unexplained by the others, so it is hard to distinguish from them. It is a warning sign for collinearity, not proof that the predictor has no outcome relationship.

18. Which heuristic suggests definite collinearity when examining pairwise correlations among predictors?

Absolute correlation equal to 0
Absolute correlation greater than 0.3
Absolute correlation greater than 0.8
Absolute correlation greater than 0.5

Absolute correlation greater than 0.8

Explication

A correlation magnitude above 0.8 is used as a heuristic for definite collinearity, while above 0.7 suggests possible collinearity. Pairwise correlations alone still may miss more complex multicollinearity.

19. Which set of checks is used to assess residual normality in multiple regression?

VIF and tolerance
Correlation matrix and histogram of predictors
rvf plot and scatterplot matrix
Normal probability plot and Shapiro-Wilk test

Normal probability plot and Shapiro-Wilk test

Explication

Residual normality is assessed with a normal probability plot and the Shapiro-Wilk test. A non-significant Shapiro-Wilk result supports approximate normality.

20. What is the main purpose of an rvpplot in multiple regression diagnostics?

To check residuals against a specific predictor for linearity
To estimate the regression intercept more accurately
To test whether residuals are independent across cases
To measure the amount of multicollinearity among predictors

To check residuals against a specific predictor for linearity

Explication

An rvpplot graphs residuals against a specific predictor to assess linearity for that predictor. It complements the global rvf plot, which is used more broadly for checking variance patterns.

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Unit goals — main aim?

Framework for statistical analyses using GLM.

Assessment tasks — components?

Data-analysis task, practical project, final exam.

Regression — definition?

Predicts a numeric outcome y from predictors x.

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