Question 1

The best part here is that we didn’t have to draw a line

Accepted Answer

Omg Yes😭😂

Question 2

How do we create the best fit line, as sometimes it is not given in the questions.

Accepted Answer

Basically, you really don't want to find the exact best fit line, because it is going to take you (and probably everyone else in the world, except computers) 1,000,000 years to find it because you have to find the absolute minimum linear regression for the line. You also have to use standard deviation, so just don't do it unless the problem tells you to eyeball it, which you can do.

Question 3

Why do you always have to draw the best fit line to determine the answer ?

Accepted Answer

Lucky for us, in this case, WE didn't have to draw the line of best fit--it was given to us.  
If we don't have a line of best fit, how do we find the rate of change?  Well, that would be how much the data increases between points, divided by the measurement increase along the x-axis, which in this case is years.

But then we have to choose points to use to find the rate of change.
Here are some of the coordinates from that graph that we can use:

`0  42`
`1  46`
`2  48`
`3  54`
`4  47`
`5  48`
`6  56`
`7  58`
`8  54`
`9  50`

If we choose 0 years and 1 year, the percentages are 42 and 46
The calculation is (46 - 42)/(1 - 0) which is 4/1 or `4% per year`

If we choose 1 year and 4 years,  the percentages are 46 and 47
The calculation is (47 - 46)/(4 - 1) which is 1/3  or `0.33% per year`

If we choose 3 years and 4 years,  the percentages are 54 and 47
The calculation is (47 - 54)/(4 - 31) which is -7/1  or `-7.0% per year`

If we choose 2 years and 5 years,  the percentages are 48 and 48
The calculation is (48 - 48)/(5 - 2) which is 0/3  or `0% per year` (no change)

If we choose 0 years and 9 years,  the percentages are 42 and 50
The calculation is (50 - 42)/(9 - 0) which is 8/8  or `1% per year`
4% .33% -7% 0% 1% are all correctly calculated from the data points, but they are wildly different and none of them is a good answer.  THAT is why we draw a line of best fit.

In other words, we use the slope of an imaginary line that passes through the points to help us choose good points for calculating the answer.

Question 4

When given a scatterplot without the line of best fit already provided for you what is the best approach to take to find that line and the slope for that line.

Accepted Answer

use your test booklet, use your answer key as a ruler and do your best to draw a line of best fit. Once you find the slope,  just go with whats closest.

Question 5

how do we create the best fit line?

Accepted Answer

Usually they provide the best fit line, but it's basically a straight line as close as possible to as many of the points as possible. Sometimes the best-fitting line is CLEARLY not straight, in that case you draw a parabola, which is a uniform curved line, as close as possible to the points. I hope that helps :)

Question 6

how did you get 1.25 from 10%/8

Accepted Answer

Sal wants an answer in terms of percent per year, so he takes the change in y-values of the graph, 10%, and divides it by the change in x-values, 8 years. 
10 / 8 = 1 2/8 = 1 1/4 = 1.25 percent per year
Does this help?

Question 7

how to get the slope on a scatter plot

Accepted Answer

For a scatterplot on the SAT, the fastest and easiest way to get a line of best fit is to just eyeball it. The answers will be different enough from each other that errors will be slight and you can pick the closest answer. Just draw a line through the "center" of the scatterplot, or if you prefer, through the furthest-apart two points that you can find that aren't obvious outliers. Then you can calculate the slope through rise-over-run.

Course: Digital SAT Math > Unit 3

Scatterplots — Basic example

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