Final answer:
The given line of fit has a slope of -1/4 after converting to slope-intercept form, which indicates a negative correlation as the x and y variables move in opposite directions.
Step-by-step explanation:
The given line of fit equation is 2x + 8y = -4. To understand the type of correlation it represents, we should first write the equation in slope-intercept form, which is y = mx + b, where m is the slope of the line. In slope-intercept form, the sign of the slope (m) indicates the direction of the correlation between x and y.
Let's solve for y:
- 2x + 8y = -4
- 8y = -2x - 4
- y = (-2/8)x - (4/8)
- y = (-1/4)x - 1/2
The slope here is -1/4, which is a negative number. Therefore, according to the data, as x increases, y decreases and vice versa, indicating a negative correlation. In scatter plots, a negative correlation is represented by a downward sloping line, just as the slope of the given equation suggests. Therefore, the correct answer is B) Negative correlation.