Unit 6 Name: Date: Hour: Sampling Distributions Section 4.1A: Drawing and Interpreting Scatter Diagrams Notes By the end of this lesson, students will be able to Draw and Interpret scatter diagrams Use the print out from the book to fill in the notes. Then complete the homework assignment. When we have two variables, they could be related in one of several different ways They could be unrelated One variable (the or variable) could be explained by the other (the or variable) One variable could be thought of as causing the other variable to change In this chapter, we will be looking at explanatory and response variables. Sometimes it is not clear which variable is the explanatory variable and which is the response variable Sometimes the two variables are related without either one being an explanatory variable Sometimes the two variables are both affected by a third variable, a, that had not been included in the study An example of a lurking variable A golf pro wanted to learn the relation between the club-head speed of a golf club (measured in miles per hour) and the distance (in yards) X = Club head speed (mph) Y = Distance (yards) A variable that may affect the response variable, but is excluded from the analysis. Possible lurking variables could include:,,, and
Distance (yards) Data Analysis & Probability The most useful graph to show the relationship between two quantitative variables is the. Each individual is represented by a point in the diagram The explanatory (X) variable is plotted on the horizontal scale The response (Y) variable is plotted on the vertical scale Example 1: Plot the following data from the Golf example above on the provided coordinate plane. Club-Head Speed (mph) Distance (yards) 100 257 102 264 103 274 101 266 105 277 100 263 99 258 105 275 3.5 285 280 3 2.5 275 270 2 1.5 265 260 1 0.5 255 0 98 99 100 101 102 103 104 105 Club Head Speed (mph) There are several different types of relations between two variables A relationship is when, plotted on a scatter diagram, the points follow the general pattern of a line A relationship is when, plotted on a scatter diagram, the points follow a general pattern, but it is not a line A relationship has when, plotted on a scatter diagram, the points do not show any pattern Linear relations can be either (the points slants upwards to the right) or (the points slant downwards to the right) Nonlinear relations have points that have a trend, but they do not look a line
When two variables are not related There is no linear trend There is no nonlinear trend Changes in values for one variable do not seem to have any relation with changes in the other Nonlinear relations and no relations are VERY different ~ Nonlinear relations are definitely patterns just not patterns that look like lines ~ No relations are when no patterns appear at all Example 2: Look back at your scatter plot in example one. What type of relation would you say exists between club-head speed and distance?
Name: Date: Hour: Unit 6 Sampling Distributions Section 4.1A: Drawing and Interpreting Scatter Diagrams Homework 1. Explain what is meant by a lurking variable. Provide an example. 2. What does it mean to say that two variables are positively associated? 3. What is the difference between an explanatory and a response variable? For problems 4-7, determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. 4. 5. 6. 7.
8. A pediatrician wants to determine the relation that may exist between a child s height and head circumference. She randomly selects 11 three-yearold children from her practice, measures their height and head circumference, and obtains the data shown in the table. a. If the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable (x) and which is the response variable (y). b. Draw a scatter diagram of the data, labeling the axes as you described in part a. c. Comment on the type of relation that appears to exist between the height and head circumference of a child on the basis of the scatter diagram. 9. A researcher wants to know if the gestation period of an animal can be used to predict life expectancy. She collects the following data: a. Suppose the researcher wants to use the gestation period of an animal to predict its life expectancy. Determine which variable is the explanatory and which is the response variable. b. Draw a scatter diagram labeling the axes as you described in part a. c. Comment on the type of relation.