LSRL

Chapter 4

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)

Mathy = mx+b

• All the points are in the line • For example y =3x + 2 will give us exactly

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

Line Math y = mx + b• Given two points (1, 5) and (2, 8)• A) find the equation of the line y=mx+bTo 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)

Line Math y = mx + b• Given two points (1, 5) and (2, 8)• A) find the equation of the line y=mx+bTo 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

Line Math y = mx + b• Given two points (1, 5) and (2, 8)• A) find the equation of the line y=mx+bTo Find the equation first you need to find the slope, then the y-intercept (0,b)

So slope m= 3y-intercept is (0,2) so b = 2

Now write the equation y = 3x + 2

Math• 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 = -6 + 2 = -4

• 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)

Line Stats

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)

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

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:

Example 1 Find the LSRL

Mean StDev Nicotine (x) 0.9414 0.3134 CO (y) 12.379 4.467

Here is the LSRL Least Square Regression Line

Here is the slope

Here is the y-intercept

correlation of nicotine and CO r = 0.863

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”

Slope = 12.31 ppm (parts per million).

For every one mg of nicotine increase, the ppm level in carbon monoxide increases on average by 12.31 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.

Example 1 In Context

Example 2 In Context

• Slope= 14.21 mg.• For every one mg of nicotine increase, the tar

level will increase on average by 14.21 mg.• y-intercept = (0, -1.271 mg)• When the nicotine level is at 0 mg, then the tar

level equals to -1.271mg. In this context the y-intercept does not make sense because it is not possible to contain a negative amount of tar.