Unit 5, Day 1: Students will use the line of best fit to find equations of lines.

Line of best fit is a line on a graph that shows the general direction that a group of points seem to be heading. It is used in everyday life to predict an amount of something.

Tips: If the dots form an almost perfect line, connect the 2 farthest points and try to touch all the points with that same line.

Example: The following table describes data for the number of people using a swimming pool over 8 days in summer and the corresponding maximum temperature (in degrees Celsius) on each day.

a.  Draw a scatterplot for this set of data.
b.  Draw a line of best fit through the data by eye.
c.  Is the line positive or negative?
d.  Are the dots close or spread apart?
e.  Use the line of best fit to predict the swimming pool attendance where the daily maximum temperature is:
(i)  18ºC          (ii)  30ºC           (iii)  40ºC

Solution:

a.  The scatterplot is obtained by plotting y against x, as shown below.

b.  A line of best fit by eye is drawn through the scatterplot so that an equal number of points lie on either side of the line and/or the sum of the distances of the points above the line are roughly equal to the sum of the distances below the line.

c.  It is clear that y increases as x increases. So, the association between the variables is positive.

d.  The data is spread about the line. So, the association between the variables is weak.

e.
(i)  When x = 18, y = 260
     So, about 260 people are expected to attend the swimming pool.

(ii)  When x = 30, y = 400
      So, about 400 people are expected to attend the swimming pool.

(iii)  When x = 40, y = 520
       So, about 520 people are expected to attend the swimming pool.

http://www.mathsteacher.com.au/year10/ch16_statistics/09_linebestfit/24line.htm

a.) Graph this table of the amount of ice cream sold depending on the temperature of the weather:

Day	Temperature (ºC) x	Number of Ice Cream Sold y
1 2 3 4 5 6 7 8	21 23 25 27 29 31 33 35	407 418 434 479 512 515 526 540

b.) Draw the line of best fit.

c.) Is the line positive or negative? Why?

a.)
b.)

 

c.) The line of best fit is positive because it increases and keeps increasing.