Deck 9: The Linear Model Regression

Question 1

Typically, what is the minimum number of case per predictor?

A) 10-15
B) 5-10
C) 0-5
D) 15-20

Answer 1

A

Question 2

The difference between each observation (i.e. hours of training and competition score) and the model fitted to the data (i.e. all observations) is known as

A) Residual
B) Difference
C) Offset
D) Disparity

Answer 2

A

Question 3

Which of the following apply to multiple linear regression? (You may select more than one answer.)

A) Multiple outcome variables
B) Multiple predictor variables
C) A single predictor variable
D) A single outcome variable

Answer 3

B, C AND D

Question 4

Using the equation identified in Q2, calculate the potential score in a diving competition if they have amassed 250 hours of training in the 12 months leading up to the competition. Assume m = .1016 and c = 22.5.

A) 48 points
B) 52 points
C) 58 points
D) 60 points

Question 5

Percentage body fat cannot be measured directly, so it has to be predicted from a series of skinfold measures. Suppose seven sites were measured (triceps, chest, midauxillary, subscapular, suprailiac, abdominal and thigh). How many participants should be recruited for a multiple regression to be performed?

A) 105
B) 155
C) 85
D) 65

Question 6

Typically, research studies in sports science tend to recruit fairly small sample groups (less than 20), but what magnitude of effect can random data have on a data set?

A) Strong effect
B) Weak effect
C) No measurable effect
D) Weak to medium effect

Question 7

What happens to the line of best fit if participant 4 scored 22, instead of 95, and participant 17 scored 20 as opposed to 90 in the diving competition?

A) The line of best fit has become flatter.
B) The line of best fit has become steeper.
C) The line of best fit has the same angle but is generally above the observations.
D) The line is relatively unaffected by the change in data.

Question 8

Having obtained a scatterplot to inspect the data, you suspect that the results for participants 4 and 17 are outliers. What should you do?

A) Remove the cases so that the model is more representative of the majority of observations.
B) Perform a series of diagnostic tests on the data such as Cook's distance or Mahalanobis distance.
C) Leave the data points in and incorporate the Fick reducer variable.
D) Rerun the analysis without the observations in to see how the regression model is affected.

Question 9

The number of hours spent practising and the ability to successfully execute a specific skill (e.g. arm stand, high board dive) are related by a straight-line model: the more you practise, the better the performance of the dive. Which of the following equations best represents a 'straight line' model?

A) y = mx + c
B) y = mc + x
C) y = cm - x
D) y = cx + m

Question 10

Suppose the abdominal and subscapular skinfold sites had a high degree of collinearity. What are the implications of this when attempting to predict percentage body fat?

A) Increased standard errors of the b coefficient.
B) It limits the R value as the predictor variables account for the same variance in the outcome variable (i.e. percentage body fat).
C) It becomes difficult to decide which variable to include.
D) All of the above.

Question 11

You determine an effect size from a study to be .04. How would this effect be categorized?

A) Very weak effect
B) Medium effect
C) Medium to strong effect
D) Very strong effect

Question 12

Which of the following are assumptions of multiple linear regression?

A) A sample is representative of its population and the observations are independent.
B) Linearity exists within the data.
C) Normal distribution.
D) All of the above.

Question 13

What does c in a straight line equation represent?

A) The gradient of the straight line
B) The predictor variable
C) The intercept on the y-axis
D) The outcome variable

Question 14

What purpose does the adjusted R² value serve?

A) The variance in the outcome variable if the model was drawn from the population of the sample.
B) The variance between the predictor and outcome variable.
C) This is used to correct for the covariance.
D) It more accurately reflects the sample data.

Question 15

What does hierarchical regression refer to?

A) Known predictors of the outcome variable are entered first.
B) Known predictors of the outcome variable are entered last.
C) Known predictors of the outcome variable are entered simultaneously.
D) Variables are entered based on a mathematical formula.

Question 16

If there are key skinfold sites known to the researcher that enabled percentage body fat to be predicted, which regression method(s) should be chosen?

A) Hierarchial (blockwise entry)
B) Forced entry(Enter)
C) Stepwise
D) Backward

Question 17

What does the term 'residual sum of errors' (SS_R) represent?

A) The extent to which the line of best fit reflects the data
B) The degree of covariance that exists between the data
C) The measure of sphercity regarding the variables of concern
D) All of the above are appropriate.

Question 18

Why is the sample size so important to statistical analysis, in this case during regression analysis?

A) It provides a more reliable regression model.
B) It provides additional assurance that predictors are from a normally distributed data set.
C) It increases the chances of detecting a difference if one exists.
D) All of the above.

Question 19

What was the adjusted R² value for the diving data?

A) .329
B) .331
C) .292
D) .259

Question 20

What does m in a straight-line equation represent?

A) The gradient of the straight line
B) The predictor variable
C) The intercept on the y-axis
D) The outcome variable

Question 21

You run a correlation matrix of the seven different skinfold sites and obtain an R value of .87 for the abdominal and subscapular sites and a variance inflation factor (VIF) of 0.1. What would you deduce from these findings?

A) A high degree of collinearity is likely between these two skinfold sites.
B) A low degree of collinearity is likely between these two skinfold sites.
C) A moderate degree of collinearity is likely between these two skinfold sites.
D) These figures make it difficult to deduce firm conclusions.

Question 22

Which procedure could be used to determine whether the residuals from the proposed model are independent?

A) Durbin-Watson
B) Cook's distance
C) Mahalanobis distance
D) None of the above are appropriate

Question 23

Having developed a statistical model to predict percentage body fat, what is the purpose of conducting cross-validation?

A) To test the accuracy of the prediction.
B) To test the model on a different population.
C) To evaluate the covariance within the model.
D) To measure the degree of difference in the residuals.