1. LSRL
Chapter 4

2. Lines A line is made of infinite number of points
Between two points only one line can pass
A line needs the slope (steepness) and the y-intercept (location)

3. Math y = mx+b All the points are in the line
For example y =3x + 2 will give us exactly

4. Math Given two points find A) the equation of the line y=mx+b
B) Graph the line
C) predict the value of y when x= -2

5. Line  Math  y = mx + b Given two points (1, 5) and (2, 8)
A) find the equation of the line y=mx+b
To Find the equation first you need to find the slope, then the y-intercept (0,b)
To find slope use
So slope m=3
Then you need to find the y-intercept (0,b)

6. Line  Math  y = mx + b Given two points (1, 5) and (2, 8)
A) find the equation of the line y=mx+b
To Find the equation first you need to find the slope, then the y-intercept (0,b)
So slope m=3
Then you need to find the y-intercept (0,b)
Y =mx+b replace the found slope
Y= 3x +b now use one of the two points I chose (2,8)
8= 3 (2)+ b now solve for b  b= 2

7. Line  Math  y = mx + b Given two points (1, 5) and (2, 8)
A) find the equation of the line y=mx+b
To Find the equation first you need to find the slope, then the y-intercept (0,b)
So slope m= 3
y-intercept is (0,2) so b = 2
Now write the equation y = 3x + 2

8. Math y = 3(-2) + 2 = -6 + 2 = -4 Given two points (1, 5) and (2, 8)
A)Find the equation of the line
B) Graph the line
To graph the line use
A table or the two given points
C) predict the value of y when x = - 2
y = 3x + 2
y = 3(-2) + 2 = = -4

9. Line  Stats 
The Difference is that here we have too many scatter points and therefore we could make many lines.
However to decide what is the best line, we use the Least Square Regression Line approach (LSRL)
A line that minimize the distance from the observed y value in our data set to the y-predicted (that falls in the line)

10. Line  Stats  So to find Least Square Regression Line (LSRL)
You need either a software or formulas that take into account all the scatter points in our data including the variability.
Still the slope is
The y-intercept (0, b0) or (0, a)

11. Line  Stats  So to find Least Square Regression Line (LSRL)
You need either a software or formulas that take into account all the scatter points in our data including the variability.
Still the slope is
but now we use
“r” which is the correlation coefficient that tell us the strength and the direction of the scatter points,
We use Sy which tell us the variability in y (rise)
we use Sx which tell us the variability in x (run)
then fin the slope

12. Line  Stats  So to find Least Square Regression Line (LSRL)
You need either a software or formulas that take into account all the scatter points in our data including the variability.
To find the slope:
To find y-intercept:

13. Here is the y-intercept
Example 1 Find the LSRL
correlation of nicotine and CO
r = 0.863
Mean StDev
Nicotine (x)
CO (y)
Here is the slope
Here is the LSRL
Least Square Regression Line
Here is the y-intercept

14. Interpret of Slope and y-intercept in Stats
CONTEXT is the most important part
But the General form of interpretation is:
Slope For every unit increase in x, y increases on average by the slope.
Y-intercept When x = 0, then y equals “a”

15. Example 1 In Context Slope = 12.31 ppm (parts per million).
For every one mg of nicotine increase, the ppm level in carbon monoxide increases on average by ppm.
y-intercept =(0, 0.79)
When the nicotine level is at o mg then the carbon monoxide level is at .79 ppm. In this context of the y intercept it does make sense because it is a positive number and you can have 0.79 ppm of CO.

16. Example 2 In Context Slope= 14.21 mg.
For every one mg of nicotine increase, the tar level will increase on average by mg.
y-intercept = (0, mg)
When the nicotine level is at 0 mg, then the tar level equals to mg. In this context the y-intercept does not make sense because it is not possible to contain a negative amount of tar.