Deck 9: The Linear Model Regression

Question 1

The distance of cases from the model mean is called

A) Leverage values
B) Hat values
C) Standard distances
D) Mahalanobis distances

Answer 1

Mahalanobis distances

Question 2

Which of the following statements about the F-ratio is true?

A) The F-ratio is the ratio of variance explained by the model to the error in the model.
B) The F-ratio is the ratio of variance explained by the model to the total variance in the outcome variable.
C) The F-ratio is the ratio of error variance to the total variance.
D) The F-ratio is the proportion of variance explained by the regression model.

Answer 2

The F-ratio is the ratio of variance explained by the model to the error in the model.

Question 3

A researcher had a categorical variable that they wanted to include as a predictor in a regression equation. The researcher was trying to predict the success of a back pain intervention, and the categorical variable was the duration of the back pain prior to treatment, with four categories: less than 6 months, 6-12 months, 1-2 years, more than 2 years. They needed to code these variables into dummy variables for the regression using less than 6 months as their control category. Which of the following represents the correct coding scheme?

A)
B)
C)
D)

Answer 3

Question 4

The difficulty with using one regression equation to predict values in a different set of data is called

A) Shrinkage
B) Contraction
C) Reduction
D) Washing

Question 5

Which of the following statements best defines the term 'multicollinearity'?

A) When two predictors have a combined correlation coefficient of 1
B) When there are strong correlations between two or more predictors in a regression model*
C) When one predictor is a perfect linear combination of the other predictors
D) None of the above

Question 6

What is R²?

A) The percentage of variance in the predictor accounted for by the outcome variable
B) The proportion of variance in the outcome accounted for by the predictor variable or variables
C) The proportion of variance in the predictor accounted for by the outcome variable
D) The percentage of variance in the outcome accounted for by the predictor variable or variables

Question 7

Which of these statements is not true?

A) If the average variance inflation factor is greater than 1 then the regression model might be biased.
B) Tolerance values above 0.2 may indicate multicollinearity in the data.*
C) Multicollinearity in the data is shown by a variance inflation factor (VIF) greater than 10.
D) The tolerance is 1 divided by the VIF.

Question 8

What does the t-statistic test?

A) The null hypothesis that the value of b (correlation coefficient) is negative
B) The null hypothesis that the value of b (correlation coefficient) is equal to 0
C) The null hypothesis that the value of b (correlation coefficient) is equal to 1
D) The null hypothesis that the value of b (correlation coefficient) is positive

Question 9

The method of least squares is used to find out which of the following?

A) The relationship of the gradient of the line
B) The intercept of the line
C) The gradient of the line
D) The line of best fit

Question 10

A way of representing discrete variables in multiple regression is by constructing

A) Stupid variables
B) Dummy variables
C) Imitation variables
D) Faking variables

Question 11

What does the following graph show?

A) Heteroscedasticity
B) Non-linearity
C) Heteroscedasticity and non-linearity
D) Regression assumptions that have been met

Question 12

Which of the following statements about the t-statistic in regression is not true?

A) The t-statistic tests whether the regression coefficient, b, is equal to 0.
B) The t-statistic provides some idea of how well a predictor predicts the outcome variable.
C) The t-statistic can be used to see whether a predictor variable makes a statistically significant contribution to the regression model.
D) The t-statistic is equal to the regression coefficient divided by its standard deviation.

Question 13

What does the F-test measure?

A) How much the model has improved the prediction of the outcome compared to the level of inaccuracy of the model
B) How much the model is influenced by the predictors compared to the numbers of residuals
C) How much the model relies on residual mean squares compared to the inaccuracies of the predictors
D) None of the above

Question 14

For which regression assumption does the Durbin-Watson statistic test?

A) Linearity
B) Independence of errors
C) Homoscedasticity
D) Multicollinearity

Question 15

Which of the following is not a reason why multicollinearity a problem in regression?

A) It limits the size of R.
B) It makes it difficult to assess the importance of individual predictors.
C) It leads to unstable regression coefficients.
D) It creates heteroscedasticity in the data.

Question 16

When making assumptions about regression analysis, which of the following is not considered to be true?

A) Homoscedasticity
B) Independent errors
C) Perfect multicollinearity
D) Categorical or quantitative variable type

Question 17

A researcher summarizes her results of research into the use of a specific type of inhaler for asthma sufferers as follows: 'predictors significantly favoured inhaler use (adjusted R²= .38; p = .015). Inhaler A was the strongest predictor of improved breathing (β = .39; p = .001) followed by inhaler B (β = .28; p = .0015)'. Which of the following would be the best interpretation of the variables in relation to these results?

A) 39% of the variation in inhalers
B) 28% of the variation in inhalers
C) 38% of the variation in inhalers
D) None of the above

Question 18

What is multicollinearity?

A) When predictor variables correlate very highly with each other.
B) When predictor variables have a linear relationship with the outcome variable.
C) When predictor variables are correlated with variables not in the regression model.
D) When predictor variables are independent.

Question 19

Which of the following statements about outliers is not true?

A) Outliers are values very different from the rest of the data.
B) Outliers bias the mean.
C) Outliers bias regression parameters.
D) Outliers are influential cases.

Question 20

In a research experiment that looks at the levels of anxiety in relation to recordings of blood pressure, what factors would cause your data to be biased due to the effect on the estimated regression coefficients?

A) Residuals
B) Outliers
C) Residual sum of squares
D) None of the above