Flash Forward

1
Flash Forward

• When Tuesday June 17, 2008 915AM
• Where Mahopac High School GYM
• Occasion NYS Integrated Algebra
• Situation You just received your test, turned
  on your graphing calculator and realized that
  your brother or sister needed the batteries for
  their PSP over the weekend!!!!!!!!

2
What do you Do?

1. Jump out of your seat and run screaming from the
   room!!
2. Start chatting with the other Math teachers to
   see who you want to take math with next year.
3. Start making plans for some serious payback to
   your sister or brother.
4. Remember todays lesson that we can do regression
   manually!!!

3
Scatter Plots and Regression Lines Without a
Calculator
4
What is a Line of Best Fit?

• When data is displayed with a scatter plot, it is
  often useful to attempt to represent that data
  with the equation of a straight line for purposes
  of predicting values that may not be displayed on
  the plot.Such a straight line is called the
  "line of best fit." It may also be called a
  "trend" line.
• A line of best fit is a straight line that best
  represents the data on a scatter plot.  This
  line may pass through some of the points, none of
  the points, or all of the points.

5
Is there a relationship between the fat grams and
the total calories in fast food?
                          
Sandwich Total Fat (g) Total Calories
Hamburger 9 260
Cheeseburger 13 320
Quarter Pounder 21 420
Quarter Pounder with Cheese 30 530
Big Mac 31 560
Arch Sandwich Special 31 550
Arch Special with Bacon 34 590
Crispy Chicken 25 500
Fish Fillet 28 560
Grilled Chicken 20 440
Grilled Chicken Light 5 300
Can we predict the number of total calories based
upon the total fat grams?
Let's find out! 1.  Prepare a scatter plot of the
data.

6
Is there a relationship between the fat grams and
the total calories in fast food?
Can we predict the number of total calories based
upon the total fat grams?
                          
Let's find out! 2. Using a straight edge,
position it so it is as close to all the points
as possible.

7
Is there a relationship between the fat grams and
the total calories in fast food?
Can we predict the number of total calories based
upon the total fat grams?

• Find two points that you think will be on the
  "best-fit" line. 
• Click to see best fit
• I chose the points (9, 260) and (30, 530).  You
  may choose different points. 
• Calculate the slope of the line through your two
  points.            

8
Is there a relationship between the fat grams and
the total calories in fast food?
Can we predict the number of total calories based
upon the total fat grams?

• Write the equation of the line using the slope
  from step 5.
• Substitute x and y
• Solve for b.

Final Regression Equation

9
Is there a relationship between the fat grams and
the total calories in fast food?
Can we predict the number of total calories based
upon the total fat grams?
Final Regression Equation
Lets predict how many calories a sandwich would
have if it had 22 grams of fat?
So we would predict that a sandwich with 22 grams
of fat would have 427 calories.

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A Word About Predictions

• If you are looking for values that fall within
  the plotted values, you are interpolating.
• If you are looking for values that fall outside
  the plotted values, you are extrapolating.  Be
  careful when extrapolating.  The further away
  from the plotted values you go, the less reliable
  is your prediction.

11
Lets Practice with This One!
Write the regression equation and predict the
value of the investment 10 years after the
initial purchase.
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Practice with Round Robin

1. Each Student has a colored pencil and a piece of
   graph paper.
2. Each student does step a (draw the scatter plot)
   of a different problem (windows (1), doors (2)
   other (3) initial their work.
3. Pass your paper in a clockwise direction
   coaches the person if the work received was
   incorrect, praise when correct.
4. Each student now completes step b (draw a line of
   best fit) and initials their work.
5. Pass your paper in a clockwise direction
   coaches the person if the work received was
   incorrect, praise when correct.
6. Each student now completes step c (determine the
   equation of the line of best fit) and initials
   their work.
7. Pass your paper in a clockwise direction
   coaches the person if the work received was
   incorrect, praise when correct.
8. Each student now completes step d and uses the
   prediction equation to estimate an answer and
   initials their work.