Question
The scatterplot above shows the total number of home runs hit in major league baseball, in ten-year intervals, for selected years. The line of best fit for the data is also shown. Which of the following is closest to the difference between the actual number of home runs and the number predicted by the line of best fit in 2003?
- 250
- 500
- 750
- 850
Hint:
Hint:
Line of best fit refers to a line through a scatter plot of data points that best approximates the given set of data. We are given the total number of home runs hit in major league baseball, in ten-year intervals, for selected years. We need to focus on year 2003 only. Carefully see where the point is plotted on the vertical axis and calculate the difference accordingly.
The correct answer is: 750
From the graph, we observe that the point on the y-axis or the number of home runs for the year 2003 is between 5000 and 5500.
If the point was exactly at the centre on the line, then it would give us the midpoint, which is given by 
But, if we look carefully, the point is a little below the midpoint.
So, we take the value to be approximately 5250
The approximated number of homeruns in the year 2003= 5250
Next, the line of best fit intersects the vertical line at year 2003 at 4500 homeruns in the horizontal.
The number of homeruns predicted by the line of best fit = 4500
Now, the difference between the actual number of home runs and the number predicted by the line of best fit in 2003=
Thus the correct answer is C)
Note:
A line of best fit is also called a trendline. The equation of a line of best fit can be represented as y = m x + b , where m is the slope and b is the y-intercept. This is the equation of a line. It is a line that minimizes the distance of the actual homeruns from the predicted homeruns.
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