Linear Regression Quiz
Questions: 16 · 10 minutes
1. A model predicting weekly sales from advertising is ŷ = 200 + 15x, where x is advertising spending in hundreds of dollars. How should the slope be interpreted?
Weekly sales are always 15 units.
Advertising rises by $15 whenever sales rise by one unit.
Each additional $100 of advertising is associated with an estimated increase of 15 sales units.
Advertising explains 15% of the variation in weekly sales.
2. If x is work experience measured in years and y is salary measured in dollars, what are the units of the regression slope?
Years per dollar
Dollar-years
Dollars per year
A unitless proportion
3. For simple linear regression with an intercept, how is R² related to the Pearson correlation r between x and y?
R² equals 1 − r.
R² equals r only when the slope is positive.
R² equals r².
R² and r are unrelated because they use different variables.
4. A fitted equation is ŷ = 5 + 2x. What outcome does the model predict when x = 6?
17
12
16
7
5. An analyst replaces x with a centered predictor x − x̄ and refits a simple regression with an intercept. What should happen?
The slope and fitted values stay the same, while the intercept changes to represent the prediction at the mean of x.
Both the slope and fitted values change because every predictor value is different.
The intercept stays the same, while the slope changes units.
The slope becomes zero because the centered predictor has mean zero.
6. A fitted model predicts a value of 42, but the observed value is 47. What is the residual, using observed minus predicted?
Positive 5
Negative 5
Positive 42
Positive 89
7. Which observation is most likely to be influential in a simple linear regression?
A point near the center of the predictor range that lies close to the fitted line
A duplicated observation located near the means of both variables
A point with an unusual outcome but an ordinary predictor value that barely changes the fitted line
A point far from the other predictor values that noticeably changes the fitted line when removed
8. Which statement best distinguishes correlation from simple linear regression?
Correlation applies only to numerical variables, while regression can use any variables without encoding them.
Correlation summarizes the direction and strength of a linear association, while regression models an outcome as a function of a predictor.
Correlation measures causation, while regression measures association.
Correlation is used for samples, while regression is used only for entire populations.
9. A regression line was fitted using temperatures from 5°C to 30°C. Why should a prediction at 80°C be treated cautiously?
Regression equations cannot produce predictions above the largest observed outcome.
It is an extrapolation, and the observed linear pattern may not continue that far beyond the data.
Predictions are valid only at predictor values already present in the sample.
A predictor must always be converted to a percentage before predicting outside its range.
10. What does ordinary least squares minimize when fitting a simple linear regression line?
The correlation between fitted values and outcomes
The sum of the absolute predictor values
The sum of the squared residuals
The number of observations above the line
11. A regression model has R² = 0.64. Which interpretation is most appropriate?
The predictor causes 64% of the outcome.
The correlation between the variables must be 0.64.
The model's predictions are correct 64% of the time.
The model accounts for 64% of the observed variability in the outcome within the analyzed data.
12. A residual plot shows a clear U-shaped pattern around zero. What does this most strongly suggest?
The outcome and predictor have exactly zero correlation.
A straight-line model is missing a systematic curved relationship.
The residuals have been calculated with the wrong sign.
The fitted line necessarily has the wrong intercept but the correct slope.
13. Residuals are tightly clustered at low fitted values but spread out like a funnel at high fitted values. Which regression condition is most directly in question?
The predictor has a nonzero mean.
The fitted line passes through the sample means.
The outcome and predictor are measured in the same units.
The residual variance is constant across fitted values.
14. A strong positive regression relationship is found between study time and exam scores in observational data. What can be concluded about causation from this result alone?
Study time definitely causes higher scores because the fitted slope is positive.
The variables are associated, but the regression alone does not establish that study time causes the score difference.
Higher scores definitely cause students to study longer.
Causation is established whenever R² exceeds 0.50.
15. In a simple linear regression with one predictor, the correlation between x and y is −0.70. What must be true of the fitted slope?
It equals −0.70 in the original measurement units.
It equals 0.49 because the correlation is squared.
Its sign cannot be determined from the correlation.
It is negative.
16. A model is ŷ = 120 + 8x, and all observed x-values are between 10 and 50. What is the best interpretation of the intercept, 120?
It is the predicted outcome at x = 0, but it may have little practical meaning because zero lies outside the observed range.
It means the outcome increases by 120 for every one-unit rise in x.
It is the predicted outcome when x equals 10, the smallest observed value.
It is the average observed outcome across all x-values.