Entry: 1
Line of best fit.
Here in this blog entry, we will show you how to properly find the line of best fit.
Firstly, You need your data points, preferably set up in a nice chart like this:

Sandwich	Total Fat (g)	Total Calories
Hamburger	9	260
Cheeseburger	13	320
Quarter Pounder	21	420
Quarter Pounder with Cheese	30	530
Big Mac	31	560
Arch Sandwich Special	31	550
Arch Special with Bacon	34	590
Crispy Chicken	25	500
Fish Fillet	28	560
Grilled Chicken	20	440
Grilled Chicken Light	5	300

Then, You can prepare a scatter plot of the points. In this demonstration, a piece of spaghetti was used to create the straight line, like so.



After that, you should pick the two best points that follow the trend of all the points and set the spaghetti, or best fit line, through them.



For this example, I chose points (9,260) (30,530)
You then can calculate the slope through your two points, like this
. (Note the answer in this image was rounded to the third decimal place, and is usually unnecessary )
You are then able to write the equation of a line!

You can now predict how the line would continue to grow, good job!

Here is a small practice quiz, to help you out if you feel like you need some extra practice the key is below:

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 association positive or negative?
d.  Is association weak or strong?
e.  Use the line of best fit to predict the swimming pool attendance where the daily maximum temperature is:
(i)  18 ºC          (ii)  30 ºC           (iii)  40 ºC
































  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.