Flash Forward

Flash ForwardFlash ForwardWhen: Tuesday June 17, 2008 9:15AM

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!!!!!!!!

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 today’s lesson that we can do regression manually!!!

Scatter Plots and Regression Lines Without a Calculator

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.

Is there a relationship between the fat grams and the total calories in fast food?

Sandwich Total Fat (g)

Total Calorie

s

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.


Can we predict the number of total

calories based upon the total fat grams?

650

600

550

500

450

400

350

300

250

200

150

100

50

-50

5 10 15 20 25 30 35 40 45

Let's find out!2. Using a straight edge, position it so it is as close to all the points as possible.


Can we predict the number of total calories based upon the total fat grams?

3. Find two points that you think will be on the "best-fit" line.

Click to see best fit

4. I chose the points (9, 260) and (30, 530). You may choose different points.

5. Calculate the slope of the line through your two points.

12

12

xx

yym

930

260530

m

857.1221

270

m

m



6. Write the equation of the line using the slope from step 5.

Substitute x and ySolve for b.

bxy 857.12

b )30(857.12530

b 71.385530b29.144

Final Regression Equation: 29.144857.12 xy

bmxy



Final Regression Equation: 29.144857.12 xy

Lets predict how many calories a sandwich would have if it had 22 grams of fat?

29.144)(857.12 22y

1.427y

So we would predict that a sandwich with 22 grams of fat would have 427 calories.:

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.

Let’s Practice with This One!

Write the regression equation and predict the value of the investment 10 years after the initial purchase.

Practice with Round Robin1. 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.


6. Each student now completes step c (determine the equation of the line of best fit) and initials their work.


8. Each student now completes step d and uses the prediction equation to estimate an answer and initials their work.

Flash Forward

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