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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
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