Welcome to the Multiple Linear Regression Module quiz where we challenge your growing knowledge with a fresh set of 15 fiendish questions. Click VIEW FEEDBACK when you’re ready to see the answers. When you want to move on just click EXIT QUIZ. Enjoy!

1. You want to construct a multiple linear regression model that predicts a pupil’s score on a reading test (%) based on a number of important factors. Sort the following variables according to how you will use them in your model:

Factors

Continuous Explanatory

Dichotomous Explanatory

Dummy Explanatory

Outcome

Pupil Gender

Geographic region of school (6 categories)

Pupil Ethnicity (8 categories)

Income of family (£)

Hours per week spent reading

Reading Test Score (%)

Free school meal eligibility (yes/no)

2. Imagine that each of the squares below represents a variable. The two diagrams represent models which both explain 75% of the variance in the outcome. Which looks to be the more parsimonious model?

Model A Model B

3. Data from a record of parental occupation is divided into 9 nominal categories. It looks like a good explanatory variable for your regression analysis so you decide to break it into dummy variables. How many Dummy variables will you need to create?

4. A multiple linear regression with two Explanatory variables is carried out, explaining 70% of the total variance in the outcome. Variable A uniquely accounts for 30% of the total variance and Variable B for 25% of the total variance. What accounts for the remaining 15% of variance which has been explained?

A third predictor variable, Variable C Variance shared between Variable A and Variable B Error in the measurement of Variable A and Variable B

5. Imagine a regression model which has a pupil’s score on a cognitive ability test as the outcome variable and three predictor variables: gender (0 = girl, 1 = boy), recent maths’s test score (%) and recent english test grade (0-20). The coefficients for the model are shown below.What would be the predicted score on the cognitive ability test for a girl who scored 80% at Maths and 10 at English?Tip: The regression formula is on Page 2.2. A calculator might help if your mental arithmetic is as bad as ours…

6. Graphs A and B are P-P plots and can be used to ascertain whether or not the residuals for your regression analysis are normally distributed.Which of the two P-P plots might give you cause for concern?

Plot A Plot B

7. If a case has a high residual statistic, what does this suggest about the accuracy of the model for predicting that case’s score on the outcome measure?

Nothing, the residual statistic is not relevant The outcome for the case is accurately predicted by the model The outcome for the case is poorly predicted by the model The case is statistically significant

8. Is it possible to talk sensibly about a main effect for a variable if that variable is involved in an interaction with another explanatory variable?

Yes No Sometimes

9. Two regression models are completed, both of which include interaction terms. Which of these two line graphs suggests an interaction effect is occurring between variable X (x-axis) and Variable Z (represented by the different coloured lines)? The mean predicted score on the outcome varible is on the Y-axis.

Graph A Graph B

10. Drag the correct statements into the relevant box for each term

Statements

Multicollinearity

Homoscedasticity

Outlier

Examining a scatterplot of residuals against predicted outcome can help you identify this issue

The variance of the residuals is the same at each level of the predictor variable(s)

A single case which has a disproportionately strong influence over your regression model

The 'Cook's distance' statistic can be used to look for this issue

The 'variance inflation factor' (VIF) can be used to identify this issue

Two or more predictor variables are highly correlated with one another

11. A multiple linear regression using standardised age 14 exam score as an outcome variable was carried out. The reference category for the ethnicity variables is White-British. Males were coded as ‘0’ and females as ‘1’. Social class is an ordinal variable with 0 representing the most affluent homes and 8 the least affluent homes).Which of the following two statements are true about the coefficients table:

Females score 1.234 less marks than males after ethnicity and social class are accounted for White-British males from the most affluent social class score 7.180 on the exam at age 14 Black carribean students score 4.251 less on the exam at age 14 after gender and social class are taken into account There are no differences in score between the 8 categories of social class after ethnicity and gender are taken into account

12. In the regression table for the question above which of the ethnic categories do not differ from the White British category to a statistically significant level?

Mixed heritage Indian Pakistani Bangladeshi Black Carribbean Black African Any other ethnic group

13. Interaction terms were added to the regression model from the question above. Which of the following statements about the regression coefficients table shown below are true?

Attainment for White-British students decreases 1.836 marks with each unit increase in SEC (as the social class becomes less affluent) For Bangledeshi students attainment increases by 1.079 with each unit increase in SEC (as the social class becomes less affluent) For Bangledeshi students attainment decreases by -0.757 (-1.836 + 1.079) with each unit increase in SEC (as the social class becomes less affluent) There is an interaction effect between ethnicity and social class There are no main effects

14. We can be 95% certain that the first coefficient in the list below would not have a value of less than -7.299 if we repeated the regression analysis with another sample randomly drawn from the same population

True False

15. A regression analysis was completed in two blocks, the second of which added interaction terms to the explanatory variables included in the first model. Did the addition of the interaction terms improve the amount of variance explained to a statistically significant degree?

Yes No Insufficient information

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