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

Question

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

Answer 1

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.