SCATTER PLOTS ALGEBRA 1 UNIT 5 WRITING EQUATIONS

SCATTER PLOTS ALGEBRA 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 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 L 1 and the data values from foot length in L 2. • Once all data values are entered press 2 nd 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 5 k. 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 January Average time (minutes) 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 3 4 5 10 16 22 26 15 20 35 36 80 100 120 180

Day 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 20 th day of my training? 1 2 3 4 5 6 7 8 Ice Cream (oz) 20 25 35 45 45 35

QUESTIONS?