Determine the strength and direction of the line of best fit given the table below

Correlation coefficient. Strength. Direction of
Line of best
Fit
0.1247833
-0.9887632
0.79283524
-0.000001235
-0.59725562
Choices
Negative slope
No correlation
Strong positive
Weak positive
Positive slope
Strong negative
No slope
Weak negative

1 answer

To determine the strength and direction of the line of best fit based on the provided correlation coefficients, we can analyze each value using general guidelines for interpreting correlation coefficients (r):

  1. Strength:

    • Strong Correlation: |r| ≥ 0.7
    • Weak Correlation: 0.3 < |r| < 0.7
    • No Correlation: |r| < 0.3
  2. Direction:

    • Positive slope: r > 0
    • Negative slope: r < 0
    • No slope: r = 0

Here’s the analysis for each correlation coefficient given:

  1. 0.1247833:

    • Strength: Weak because |0.1247| < 0.3
    • Direction: Positive slope (since the value is positive).
  2. -0.9887632:

    • Strength: Strong because |-0.9887| ≥ 0.7
    • Direction: Strong negative slope (since the value is negative).
  3. 0.79283524:

    • Strength: Strong because |0.7928| ≥ 0.7
    • Direction: Positive slope (since the value is positive).
  4. -0.000001235:

    • Strength: No correlation because |-0.000001235| < 0.3
    • Direction: No slope (since it is very close to zero).
  5. -0.59725562:

    • Strength: Weak because |-0.5973| < 0.7 but > 0.3
    • Direction: Weak negative slope (since the value is negative).

Summary:

  • 0.1247833: Weak positive
  • -0.9887632: Strong negative
  • 0.79283524: Strong positive
  • -0.000001235: No correlation
  • -0.59725562: Weak negative

You can select the best description for each correlation coefficient based on the above classifications.