Use correlation coefficients to determine which of the given sets of data is worst fit by its associated regression line.
a) $\{ ( 2,6 ) , ( - 4,18 ) , ( 4,2 ) \}$
b) $\{ ( 0,1 ) , ( 1,0 ) , ( 2,1 ) \}$
c) $\{ ( 0,0 ) , ( 5 , - 5 ) , ( 2 , - 2.2 ) \}$

A)a
B) b and c
C) c
D) a and b
E) b

Question

Use correlation coefficients to determine which of the given sets of data is worst fit by its associated regression line.  
a) $\{ ( 2,6 ) , ( - 4,18 ) , ( 4,2 ) \}$ 
b) $\{ ( 0,1 ) , ( 1,0 ) , ( 2,1 ) \}$ 
c) $\{ ( 0,0 ) , ( 5 , - 5 ) , ( 2 , - 2.2 ) \}$

A)a
B) b and c
C) c
D) a and b
E) b

Quizplus · Accepted Answer

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where values close to 1 or -1 indicate a strong linear relationship, and values close to 0 indicate a weak linear relationship. A perfect linear relationship has a correlation coefficient of exactly 1 or -1. To determine the worst fit by its associated regression line, we look for the set of data with a correlation coefficient closest to 0, indicating the weakest linear relationship.For set a), the points do not align in a clear linear pattern, suggesting a weak linear relationship. However, without calculating the exact correlation coefficients for each set, it's challenging to visually determine which has the weakest linear relationship.Set b) has points that form a pattern that does not suggest a strong linear relationship, as the middle point deviates from a straight line that could connect the other two points.Set c) has points that suggest a negative linear relationship, as the values decrease together, indicating a stronger linear relationship compared to set b).Therefore, without calculating the exact correlation coefficients, set b) is expected to have a correlation coefficient closer to 0 compared to the other sets, indicating it is the worst fit by its associated regression line. This is because its points suggest a pattern that deviates most from a straight line, indicating a weaker linear relationship.

Use Correlation Coefficients to Determine Which of the Given Sets {(2,6),(−4,18),(4,2)}\{ ( 2,6 ) , ( - 4,18 ) , ( 4,2 ) \}{(2,6),(−4,18),(4,2)}

Use Correlation Coefficients to Determine Which of the Given Sets $\{ ( 2,6 ) , ( - 4,18 ) , ( 4,2 ) \}$