Question 1

Which of the following best describes the purpose of examining residual plots after fitting a linear regression model?

Accepted Answer

To check for non-linearity and violations of regression assumptions that may not be visible in the original scatterplot.

Question 2

Suppose you fit a linear regression model to data from two different subgroups, but you do not account for the groups in your analysis. What is a likely consequence?

Accepted Answer

The model may be misleading because the relationship between variables could differ between groups, violating the assumption that all data come from the same population.

Question 3

A data point in a regression analysis is far from the mean of the x-values but not unusual in the y-direction. What is this point said to have?

Accepted Answer

High leverage

Question 4

Which of the following statements about influential points in regression is TRUE?

Accepted Answer

A point is influential if omitting it from the analysis gives a very different regression model.

Question 5

Why is extrapolation using a linear regression model considered risky?

Accepted Answer

Because it assumes the relationship between x and y remains unchanged outside the range of observed data, which may not be true.

Question 6

A regression model for the median age at first marriage for men is fit using data from 1900 to 1940. The model is then used to predict the age in the year 2000, but the prediction is much lower than the actual value. What is the most likely explanation?

Accepted Answer

The model was extrapolated far beyond the range of the original data, and the relationship changed over time.

Question 7

Which of the following best explains why a strong association in a regression model does NOT imply causation?

Accepted Answer

There may be a lurking variable that affects both variables, creating an association without a direct causal link.

Question 8

In a study, the number of doctors per person and the number of TVs per person are both strongly associated with life expectancy. What is the most reasonable interpretation?

Accepted Answer

A lurking variable, such as standard of living, may be responsible for the observed associations.

Question 9

Why do scatterplots of summary statistics (such as means) tend to show less variability than scatterplots of individual data points?

Accepted Answer

Means vary less than individual values, so the scatterplot of means appears to have a stronger association.

Question 10

Which of the following is NOT a recommended practice when dealing with unusual points in regression analysis?

Accepted Answer

Remove unusual points solely to increase the R-squared value.

Question 11

A regression analysis of calories versus sugar content in cereals reveals three distinct regression lines for cereals on different shelves in a supermarket. What does this suggest?

Accepted Answer

There are subgroups in the data that may need to be analyzed separately.

Question 12

If a point has high leverage but low influence, what does this mean?

Accepted Answer

The point is far from the mean of x-values but does not substantially change the regression line.

Question 13

Which of the following is a sign that a linear regression model may not be appropriate for your data?

Accepted Answer

A residual plot shows a clear curved pattern.

Question 14

What is the main risk of using regression models based on summary data (such as means) rather than individual data points?

Accepted Answer

The strength of the association may be exaggerated, giving a false impression of how well the model fits individual data.

Question 15

Which of the following best describes the effect of a point with both high leverage and high influence on a regression model?

Accepted Answer

It can drastically change the slope and intercept of the regression line.

Question 16

A student claims that a high R-squared value in a regression model proves that x causes y. What is the best response?

Accepted Answer

A high R-squared value only indicates a strong association, not causation; there may be lurking variables.

Question 17

Which of the following is a correct interpretation of a regression slope coefficient?

Accepted Answer

It describes the relationship between x and y in the observed data, but should not be used to predict how y would change if x were changed outside the observed range.

Question 18

If a scatterplot of y versus x is not straight, what is the most appropriate action before fitting a linear regression model?

Accepted Answer

Consider re-expressing one or both variables to achieve linearity.

Question 19

Which of the following is a potential problem when restricting the range of data in a regression analysis?

Accepted Answer

The regression may appear weaker than it actually is for the full range of data.

Regression Wisdom: Advanced Concepts in Linear Regression Analysis

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