This table shows corresponding values of x and y. x 3 4 8 11 18 15 y 21 25 28 40 28 42 The data in the table represents a weak positive linear association. Which of the following could represent the correlation coefficient of the data? (1 point) Responses -0.98 -0.98 -0.3 -0.3 0.3 0.3 0.98

1 answer

The correlation coefficient (often denoted as \( r \)) measures the strength and direction of a linear relationship between two variables. Values of \( r \) range from -1 to 1, where:

  • \( r = 1 \) indicates a perfect positive linear correlation,
  • \( r = -1 \) indicates a perfect negative linear correlation,
  • \( r = 0 \) indicates no linear correlation.

Since you've mentioned that the data represents a weak positive linear association, we would expect the correlation coefficient to be a small positive number.

Among the options you provided:

  • \( -0.98 \) (a strong negative correlation)
  • \( -0.3 \) (a weak negative correlation)
  • \( 0.3 \) (a weak positive correlation)
  • \( 0.98 \) (a strong positive correlation)

The only value that represents a weak positive linear association is 0.3.

Therefore, the correct response is 0.3.