GER1000 Quiz 3 :Linear Regression

GER1000 Quiz 3 :Linear Regression
The following plot shows an outlier in both the X and Y directions.



What will happen if we remove the outlier?

Ans: The correlation between X and Y will decrease.

There is a weak positive association between numerical variables X and Y, where X ranges from 0 to 5 (inclusive). Based on the data from X and Y, the regression line is given by the equation Y = 0.25X + 2. Which of the following statement(s) is/are definitely true?

I) We can obtain the exact value of Y when X = 4.
II) The average value of Y is 4 when X = 8.
III) The correlation coefficient is 0.25.
IV) The equation provides a non-deterministic relationship between X and Y.

Ans: II and IV only

The following scatterplot shows data collected from variables X and Y.
Which of the following statements is the best description of the plot?



Ans: The correlation between X and Y is nearly 0.

The correlation for 126 pairs of (X,Y) values is 0.8. X ranges from 0 to 1. For the points with X values lying between 0.25 and 0.75, the correlation is 0.9. Is this an example of the attenuation effect?

Ans: No

Consider two tutorial classes A and B each containing 25 students. Both classes enrolled in an NUS module and sat for two tests: the midterm and the final. For tutorial class A, every student scored 5 more marks for the final compared to the midterm. For tutorial class B, every student scored 3 marks less for the final compared to the midterm. Which of the following statements is/are true?

I) For class A, the correlation between midterm and final is 1.
II) For class B the correlation between midterm and final is -1.
III) The overall correlation (combining class A and B together) between midterm and final would be less than the correlation for Class A.
IV) The overall correlation (combining class A and B together) between midterm and final would be more than the correlation for Class B.

Ans: I and III

A researcher wishes to examine the association between the number of hours students engage in gaming and their academic performance. He conducts his study in 15 schools, and calculates for each school the average number of hours students spend gaming and the average academic score of students. He notices that there is a correlation of -0.9 between the two sets of averages. He concludes that
“The correlation between gaming hours and academic score for all students from the 15 schools is -0.9”. 

What fallacy is the researcher committing here? 

Ans: Ecological

Given by another student.