Q: Given the regression equation $$Weight = -204.7 + 5.092 \ Height$$, what is the predicted weight for a person who is 70 inches tall?

$$Weight = -204.7 + 5.092 \times 70 = 151.74$$ pounds

Question 1

Which of the following is NOT a condition that must be checked before using least squares regression?

Accepted Answer

Categorical Variable Condition

Question 2

What does an R flag in Minitab indicate about an observation in a regression analysis?

Accepted Answer

The observation is an outlier with a large standardized residual.

Question 3

Given the regression equation $$Weight = -204.7 + 5.092 \ Height$$, what is the predicted weight for a person who is 70 inches tall?

Accepted Answer

$$Weight = -204.7 + 5.092 	imes 70 = 151.74$$ pounds

Question 4

Which of the following best describes the effect of a large outlier on the y-axis in a regression analysis?

Accepted Answer

It increases the standard error and decreases $$R^2.$$

Question 5

What is the formula for a standardized residual in regression analysis?

Accepted Answer

$$Z = \frac{e_i}{s \sqrt{1-h_i}}$$

Question 6

Why is it important to check the equal spread condition (homoscedasticity) in regression analysis?

Accepted Answer

To confirm that the variance of residuals is consistent across all values of x.

Question 7

If a data point has a high leverage (X flag), what does this mean?

Accepted Answer

It is far from the mean of the x-values and can influence the regression line.

Question 8

Which of the following statements about $$R^2 is $$TRUE?

Accepted Answer

$$R^2$$ measures the proportion of variability in the response variable explained by the model.

Question 9

A residual plot shows a fanning pattern as x increases. What does this suggest?

Accepted Answer

The equal spread condition is violated.

Question 10

Suppose you fit a regression model to summary data (averaged by group) instead of original observations. Which of the following is a likely consequence?

Accepted Answer

The $$R^2$$ value will typically be higher for the summary data.

Question 11

Which Minitab feature allows you to store residuals and fits after running a regression?

Accepted Answer

Storage option in the regression menu

Question 12

Why might a highly influential observation not be detected by examining only the residual plot?

Accepted Answer

It may have a small residual but a large leverage.

Question 13

Which of the following best describes the purpose of a residual plot in regression analysis?

Accepted Answer

To check for patterns that indicate violations of regression assumptions.

Question 14

If the scatterplot of residuals versus fits shows a curved pattern, what does this indicate?

Accepted Answer

The straight line condition is violated.

Question 15

Which of the following is a real-world example where regression analysis could be used?

Accepted Answer

Predicting a patient's blood pressure based on age and weight.

Question 16

What is the main reason for examining cases that do not fit the regression model well?

Accepted Answer

They can reveal important insights about the data or process.

Question 17

Which of the following is true about model selection in regression?

Accepted Answer

Meeting model conditions is necessary to select the best model.

Question 18

If a regression model has $$R^2 = 83.7$$\%$$ and another has R^2$ = 61.6\%$$, what does this suggest about the models?

Accepted Answer

The first model explains more variability in the response variable.

Question 19

Which of the following is a plausible reason for using summary data (averaged by group) in regression analysis?

Accepted Answer

To reduce the influence of individual outliers.

Least Squares Regression, Residuals, and Model Selection in Statistics

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