To determine how removing the point \((15, 7)\) would affect the slope of the line of best fit, we need to consider the position of the point relative to the line.
The given equation for the line of best fit is \( y = 0.5x + 1.5 \). Let's plug \( x = 15 \) into this equation to find the corresponding \( y \)-value on the line:
\[ y = 0.5(15) + 1.5 = 7.5 + 1.5 = 9 \]
So, the point \((15, 7)\) lies below the line of best fit, because the actual \( y \)-value (7) is less than the \( y \)-value (9) on the line.
Removing this point, which lies below the line, would cause the fit to become less influenced by points pulling it downwards, potentially increasing the overall slope of the line of best fit.
Thus, the correct answer is:
C. The slope of the line of best fit would increase because the point lies below the original line of best fit.
Clive created the scatter plot shown.
Clive finds that the line of best fit for the data has the equation y = 0.5x + 1.5. Which statement best explains how removing the point (15, 7) would affect the slope of the line of best fit?
Responses
A The slope of the line of best fit would decrease because the point lies below the original line of best fit.The slope of the line of best fit would decrease because the point lies below the original line of best fit.
B The slope of the line of best fit would decrease because the point lies above the original line of best fit.The slope of the line of best fit would decrease because the point lies above the original line of best fit.
C The slope of the line of best fit would increase because the point lies below the original line of best fit.The slope of the line of best fit would increase because the point lies below the original line of best fit.
D The slope of the line of best fit would increase because the point lies above the original line of best fit.
1 answer