Do Now:

• f(-3)

• (g ◦ f)(x)

• (f • g)(4)

3)( 42)( 2+=−+= xxgxxxf

Do Now

• Pick up the worksheet on the back table

• Take out your programming worksheet

• Begin working on the worksheet

Regressions & Solving by Graphing

Solve by Graphing

• When two functions are equal to another, we can put one function in y1

and the other in y2

• Where is the solution?

For example…

• 3(2x – 1) = 2x + 30

• Y1 = 3(2x – 1)

• Y2 = 2x + 30

• Find the intersection: 2nd�TRACE�intersect�ENTER(x3)

Try these…

7354 +=+ xx

)23(273 −=− xx

9874 +=− xx

1.

2.

3.

REGRESSIONS

Finding the BEST equation…

• First step is to turn on the diagnostic!

• 2nd ZERO

• Scroll down to “Diagnostic On”

• Press “Enter” and “Enter” again

What is the “r” value?

• The “r” value is called the linear

correlation coefficient

• It measures the strength and

the direction of a linear

relationship between two

variables.

What is the “r 2” value?

The coefficient of determination,

r2 represents the percent of

the data that is the closest to

the line of best fit. It is also

used to measure the accuracy

of the model.

How to interpret…

• -1 ≤ r ≤ 1

• 0 ≤ R2 ≤ 1

• The closer the R2 value is to 1, the

better the model.

Correlations

• Positive Correlation

r = +

•

• Negative Correlation

r = -

Correlations

• Strong Correlation

r close to 1

• Weak Correlation

r around 0.25 to .75

• No Correlation

r close to 0

Summary

Decide if the correlation is strong, weak,

positive, negative, or there is none.

Decide if the correlation is strong, weak,

positive, negative, or there is none.

Decide if the correlation is strong, weak,

positive, negative, or there is none.

Decide if the correlation is strong, weak,

positive, negative, or there is none.

Example - predict the r value,

then find it!

Find the equation of best fit…

• Input the data

• Find the R2 value for the following:• #4: LinReg

• #5: QuadReg

• #0: ExpReg

• Determine which one is CLOSEST to 1

• That is the equation of best fit!

Example 1

Example 2

Example 3

Example 4