Question

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?
a 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.
c 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.

Explanation:

Step1: Analyze the position of the point

The original line of best fit has a positive slope ($y = 0.5x+1.5$). The point $(15,7)$: when $x = 15$, the value on the line $y=0.5\times15 + 1.5=7.5 + 1.5=9$. Since $7<9$, the point $(15,7)$ lies below the original line of best fit.

Step2: Consider the effect of removing the point

If we remove a point that lies below the line of best fit, the new line of best fit will be steeper (increase in slope). Because the original line was “pulled down” by this relatively low - value point for its $x$ - coordinate. Removing it, the line will adjust to better fit the remaining points which, on average, for a given $x$ have a relatively higher $y$ - value compared to the situation when the $(15,7)$ point was included.

Answer:

C. The slope of the line of best fit would increase because the point lies below the original line of best fit.