Question 1

A data point with a large, positive residual ________________________ .

Accepted Answer

B and C are correct because a large, positive residual indicates that the actual value is much higher than the predicted value by the model, suggesting an underestimate by the model and a potential outlier that warrants further investigation.

Question 2

Which of the following plots can be used to indicate that there may be different groups in the data that should be considered separately?

Accepted Answer

All of these plots can indicate the presence of different groups within the data. A histogram of the residuals might show multiple peaks indicating different groups. Residuals vs predicted values can show patterns or clusters indicating group differences. A scatterplot with regression lines for each group directly shows the presence of different groups and how they might differ in terms of the regression relationship.

Question 3

Transformation (re-expression) is NOT done to make the ________________________ .

Accepted Answer

A

Question 4

The analysis of unusually large or small residuals can help us to ________________________ .

Accepted Answer

Analyzing large or small residuals is a crucial part of regression analysis, as it helps in identifying data points that do not fit well with the model. This can lead to the discovery of groups or patterns within the data (A), pinpointing outliers or extreme observations that may influence the model disproportionately (B), and suggesting the presence of other variables or factors affecting the relationship that were not initially considered (C). Therefore, all of these options are correct.

Question 5

When working with scatterplots of summary values ________________________ .

Accepted Answer

When working with scatterplots of summary values, such as means or averages, the variation within each group is not represented. This lack of representation of the individual data points' variability can lead to an inflated perception of the strength of a relationship, as the scatterplot might appear 'tighter' or more correlated than it actually is when considering the individual data points.

Question 6

A regression model was estimated to describe the trend in closing stock prices over 8 months.The Durbin Watson statistic was calculated as 0.5626.Using α = .01 we can conclude that there is evidence of ________________________ .

Accepted Answer

The Durbin Watson statistic ranges from 0 to 4, where a value around 2 suggests no autocorrelation, values approaching 0 indicate positive autocorrelation, and values approaching 4 suggest negative autocorrelation. A value of 0.5626 is closer to 0, indicating positive autocorrelation.

Question 7

A linear regression model was estimated to describe the trend in world population over time.Below is the plot of residuals versus predicted values.Which of the following re-expression of the data would be appropriate?

Accepted Answer

The answer of A linear regression model was estimated to...

Question 8

A regression model that showed good fit was developed recently to predict average annual pay for companies based on the percentage of female employees.Companies included in the analysis had between 40% and 80% of employees who were female.This model could safely be used to estimate average annual pay for companies ________________________ .

Accepted Answer

The model was developed for companies with 40% to 80% female employees, so it can safely be used for a company with 75% (or ¾) female employees, as this falls within the specified range. Other options are outside the model's scope or involve conditions not accounted for in the model's development.

Question 9

Which of the following Ladder of Powers is a good place to start if you are dealing with counted data?

Accepted Answer

The square root transformation is commonly used for counted data, especially when dealing with data that follow a Poisson distribution, as it helps stabilize the variance.

Question 10

Data on internet usage (per 100 inhabitants) and population were collected for a sample of 52 countries whose populations ranged from 0 to 40 million.Suppose the linear model fit to these data is used to determine Internet usage in India, a country with a population of 1,153,230,948.This would be called ________________________ .

Accepted Answer

Using the linear model to predict internet usage for India, which has a population far outside the range of the sample data (0 to 40 million), is an example of extrapolation. Extrapolation involves making predictions outside the range of the available data.

Question 11

A regression model was developed relating average annual pay to the percentage of women employed for a sample of companies.Below is the plot of residuals versus predicted values.Which of the following re-expression of the data would be appropriate?

Accepted Answer

The answer of A regression model was developed relating average...

Question 12

A residual analysis results in the finding that there are many residuals clustered closely around 0, but there is also some predicted values that have very large (>0) residuals and some that have very small (<0) residuals.This may indicate that ________________________ .

Accepted Answer

The presence of residuals clustered around 0 with some large positive and negative residuals suggests that there may be subgroups within the data that behave differently, indicating that separate analysis for these groups might be necessary.

Question 13

A regression model applied to autocorrelated data will have ________________________ .

Accepted Answer

Autocorrelation in data leads to a Durbin-Watson statistic that deviates from 2, indicating that residuals are not independent.

Question 14

Which of the following statements about the Ladder of Powers is true?

Accepted Answer

Using the Ladder of Powers can improve an analysis of relationships by transforming data to meet the assumptions of statistical methods, such as linearity and homoscedasticity.

Question 15

An outlier is a point with ________________________ .

Accepted Answer

An outlier is typically defined as a point with a y-value far from the regression model, indicating it does not fit the pattern of the other data points.

Question 16

A regression model was developed relating fiber and potassium content for a sample of cereals.The circled observation is ________________________ .

Accepted Answer

The answer of A regression model was developed relating fiber...

Question 17

A high leverage point ________________________ .

Accepted Answer

High leverage points can indeed hide in plots of residuals, be informative about the relationship between x and y, potentially should be omitted depending on the context, and can pull the regression line, affecting the slope's appearance.

Question 18

Data were collected for a sample of companies regarding their investment in quality improvement efforts and cost savings realized as a result (both measured as a percentage of sales revenue).The R² for the regression is 0.833.If the data were collected for individual departments within companies rather than at the company level, we would expect ________________________ .

Accepted Answer

Collecting data at the department level introduces more variability due to differences in departmental operations and efficiencies, likely leading to a lower R-squared value, which measures the proportion of variance in the dependent variable that can be predicted from the independent variable.

Question 19

Quarterly figures for e-commerce retail sales were obtained from the first quarter of 2001 through the fourth quarter of 2007.A regression model was estimated to describe the trend in e-commerce retail sales over time.The Durbin Watson statistic was calculated as 1.727.Using α = .01 we can conclude that there is ________________________ .

Accepted Answer

The Durbin-Watson statistic values range from 0 to 4, where a value around 2 suggests no autocorrelation, values approaching 0 indicate positive autocorrelation, and values approaching 4 suggest negative autocorrelation. A value of 1.727 is close enough to 2 to suggest that there is no evidence of positive or negative autocorrelation in the data.

Quiz 17: Understanding Residuals