Tuesday September 30-Friday October 3 2.5 Using Linear models Tuesday September 30-Friday October 3

Finish 2.1-2.4 Test

ROPES #5 Example The perimeter of a college basketball court is 80 m and the length is 1o m more than the width. What are the dimensions of the basketball court?

ROPES #5 The perimeter of a college basketball court is 96 m and the length is 14 m more than the width. What are the dimensions of the basketball court?

Chapter 2.5 Using Linear Models Discuss the above question with your partner. Be prepared to share why you made the prediction you made based on the information provided. You have two minutes to think about and discuss this.

Explore For each of the following table of values, plot the points on the graph paper provided on the worksheet, "sketch" a line across the points which best fits the data, and use this line to predict what would happen given a different value not shown in the table. You may raise your hand or talk to your neighbor if you have a question.

Time for Notes! A scatter plot is a graph that relates two sets of data by plotting the data as ordered pairs. Correlation is the strength of the relationship between data sets. You can use the scatter plot to determine the correlation between data sets. The closer the data points fall along a line with positive slope, the stronger the linear relationship the stronger the positive correlation between the two variables.

Notes continued… Let’s try! A trend line is a line that approximates the relationship between the variables, or data sets, of a scatter plot. You can use a trend line to make predictions from the data. You can also use the trend line to find two points along the line and write the equation of a line to model a real-world problem. This can be even more useful in making predictions. Let’s try! Given the following table of values, create the scatter plot of the data. Then, draw a trend line along the data. Write the equation of the trend line. Lastly, predict the y-value when x=16 X 1 2 3 7/2 4 Y -1 5

You Try Given the following table of values, create the scatter plot of the data. Then, draw a trend line along the data. Write the equation of the trend line. Lastly, predict the y-value when x=9. What about when x=20? X -3 -2 -3/2 -1 -1/2 1 3/2 2 3 Y 5/2

Exit-Slip: Turn in on your way out of class! On a sheet of paper, describe the correlation of the scatter plot to the left. Homework: ROPES 2.5 Lesson Check pg. 107 #1-6

Engage: Think about linear models… What happens when we try to predict points using trend lines? Is everyone’s prediction the same or different?   Could there possibly be a better way of regulating our trend lines so they would be the same?

When things are done out of order, do they still make sense?

When things are done out of order, do they still make sense?

Explore What you will need: Exploration Worksheet Graphing Calculator Pencil Straight Edge Do not touch the turn on or play with the calculators until instructed to do so. First, we will walk through the first problem on the worksheet. Then, you will complete the second problem on the worksheet with your partner. Only talk with your own table partner Follow the instructions step-by-step very carefully.

Explain: Problem 1- Length vs. Wingspan of a Hawk Length (in.) 21 18 24 16 19 17 Wingspan (in.) 36 41 38 46 31 39 35 LinReg y= ax+b a = b = r2 = r = What is the equation of the line from the information provided? ____________________   Plot the points on a Scatter Plot on your own sheet of graph paper. Then, graph the equation of the line.

Explain: Problem 2- Average Temperature vs. Electric Bill   Jan Feb Mar April May June July Aug Sept Oct Nov Dec Average Temp (F) 61 58 67 75 79 83 84 85 81 76 65 Electricity Bill $150 $139 $172 $205 $170 $234 $255 $245 $210 $183 $132 $110 LinReg y= ax+b a = b = r2 = r = What is the equation of the line from the information provided? ____________________   Plot the points on a Scatter Plot on your own sheet of graph paper. Then, graph the equation of the line.

Line of Best Fit The line of best fit is the trend line that gives the most accurate model of related data. The correlation coefficient, r, indicates the strength of the correlation. The closer r is to 1 or -1, the more closely the data resembles a line and the more accurate your model is likely to be.

Elaborate Plot the scatter plot Draw a trend line. Find the equation of the trend line. Use the equation of the trend line to estimate the test score (%) for a student who studies for 13 hours. Use the graphing calculator to input the points and find the line of best fit. What is the equation? Use the equation for the line of best fit to estimate the test score (%) for a student who studies for 13 hours.

Work on Homework! ROPES Section 2.5 Lesson Check pg. 107 #1-6, 14

Calculator Survey Please complete the calculator survey and hand it in before you leave the class.