SCATTER PLOTSALGEBRA 1 UNIT 5 WRITING EQUATIONS OF LINES

ACTIVITY• You are going to measure your hand size

and your foot size.• You are then going to write your results

on the board • You are then going to plot these points

on a graph like the one to the right.

SCATTER PLOT

• You have just created a scatter plot of data based on your hand and foot sizes. • A scatter plot is a graphical

representation of a relationship between a set of data.

CORRELATIONS OF SCATTER PLOTS

• A correlation is how well a set of data represents or depends on another set of data.

TYPES OF CORRELATIONS

• What do you notice about the perfect positive correlation and perfect negative correlations?• They can be estimated by a linear line!

MODEL THE DATA

• How could we model the data we got from our activity to determine the length of someone’s foot knowing the length of their hand?• We want to create a linear equation to model the data,

then we can estimate from that model the lengths of someone’s hand or foot.

HOW DO I MODEL THE DATA?

• Pencil and paper• Graphing calculators

• Which will be more accurate?

PENCIL AND PAPER• Grab a ruler or protractor from the back • Draw a line on your graph paper which touches as many

points as possible from the data collected in the activity, this is called the line of best fit. • Line of best fit is the line which best estimates all the data

collected and which will produce the most accurate estimations.

• Now use two points on your line to create an equation for your line.

PENCIL AND PAPER

• Use your equation to estimate the foot length of someone with a hand length of 9 inches.

CALCULATOR

• Grab your assigned graphing calculator from the box. • Turn the calculator on• Press STAT, then go to EDIT and press ENTER.• Two lists should come up; put the data values from the hand

length in L1 and the data values from foot length in L2. • Once all data values are entered press 2nd then MODE.

CALCULATOR

• A blank screen should be displayed. • Push STAT again, push the over button to the CALC screen.• Once on the CALC screen, go down to 4:LINREG and press

ENTER.• Press ENTER again for the calculator to run the points and a

line should come up on the screen.

CALCULATOR

• Use your equation to estimate the foot length of someone with a hand length of 9 inches.

CONCLUSIONS

• How do the pencil and paper versus the calculator estimations compare? • Lets test for a value of 6 inches.• Which was more accurate?

ERRORS IN DATA

• Why doesn’t all the data line up in a straight line so we can use a perfect linear model?• There are errors in data which can affect the outcome of

the equation• What are some of these possible errors?

EXAMPLE

• Gail is training for a 5k. The table shows her times for each month of her training program. Assume that her times will decrease linearly. Predict her running times in August and November.

Month Average time (minutes)

January 40

February 38

March 39

April 38

May 33

June 30

EXAMPLE• Baris is testing the burn

time of a new candle. The table shows how long it takes to burn candles of different weights. Assume a linear relationship exists. If a candle burns for 95 hours, what is the weight in ounces?

Candle weight (oz)

Burn Time (mins)

2 153 204 355 3610 8016 10022 12026 180

EXAMPLE• I am competing for an ice

cream eating challenge. The table shows my training schedule each day versus how much ice cream I eat that day. According to the linear regression line of best fit, how many ounces of ice cream should I eat on the 20th day of my training?

Day Ice Cream (oz)

1 202 253 304 255 356 457 458 35

QUESTIONS?