Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide INTERPRET SCATTERPLOTS Graph bivariate data. Interpret trends based on scatterplots. Draw lines and curves of best fit. OBJECTIVES

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Warm-UpWarm-Up Use a table of values and graph paper to graph the line represented by the equation y = 2x – 3. Slide 2

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3 data - Any set of numbers univariate data - single set of numbers bivariate data - Data that lists pairs of numbers and shows a relationship between the paired numbers scatterplot - graph that shows bivariate data trend - general pattern correlation - association between two variables positive correlation - value of one variable increases when the value of the other increases negative correlation - value of one variable decreases when the value of the other variable increases causal relationship - one variable caused a change in the other explanatory variable - variable which causes the change response variable - affected variable Key Terms

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Skills and Strategies Scatterplot A graph of a set of ordered pairs that may or may not show a relationship. Points graphed on a scatterplot are not connected. The position of the points are examined to determine the existence and strength of a correlation. Slide 4

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 5 Example 1 Rachael runs a concession stand at the park, where she sells water bottles. She keeps a list of each day’s high temperature and the number of water bottles she sells each day. Rachael is looking for trends that relate the daily high temperature to the number of water bottles she sells each day. She thinks these two variables might be related and wants to investigate possible trends using a scatterplot. Below is the list of her ordered pairs. (65, 102), (71, 133), (79, 144), (80, 161), (86, 191), (86, 207), (91, 235), (95, 237), (100, 243) Construct a scatterplot by hand on graph paper. Then enter the data in a graphing calculator to create a scatterplot.

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Example 1 Answer Slide 6

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 7 If the temperature reaches 68 degrees Fahrenheit tomorrow, about how many water bottles do you predict will be sold? Explain. CHECK YOUR UNDERSTANDING

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 8 Example 2 Rachael wants to interpret the trend shown in the scatterplot. What do you notice about the relationship between temperature and water bottle sales? Is there an explanatory variable and a response variable?

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 9 A local coffee shop sells hot chocolate. The manager keeps track of the temperature for the entire year and the hot chocolate sales. A scatterplot is graphed with temperature on the horizontal axis and hot chocolate sales on the vertical axis. Do you think the scatterplot shows a positive or negative correlation? Is there causation? Explain. CHECK YOUR UNDERSTANDING

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 10 Determine if the following scatterplot depicts a positive correlation or a negative correlation. EXAMPLE 3

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 11 A local medical school is studying growth of students in grades 1–12. The height of each student in inches and the length of each student’s foot in centimeters is recorded, and a scatterplot is constructed. Do you think the scatterplot shows a positive correlation or a negative correlation? Is there causation? CHECK YOUR UNDERSTANDING

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 12 An elementary school principal compiled the following data about ten students at Compsett Elementary School. The first number represents a student’s height in inches. The second number is the student’s reading level. Create a scatterplot of the data. Do you think a person’s height causes a higher reading level? EXAMPLE 4

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Example 4 Answer Slide 13

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 14 Think of an example of data that might have a negative correlation but there is no causation. CHECK YOUR UNDERSTANDING

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 15 The scatterplot shows the relationship between the number of text messages made by each of ten juniors while studying for Mr. Galati’s chemistry test last week and their scores on the test. Describe the trends you see in the data. EXAMPLE 5

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 16 Students in a biology class measure the circumference and diameter of every tree on the school property. The students create a table of ordered pairs and plan to draw a scatterplot. Should there be a positive correlation, a negative correlation, or no correlation? CHECK YOUR UNDERSTANDING

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. ApplicationsApplications Pages 68 – 69, #2 – 8 even Slide 17