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slide2

A medical study finds that short women are more likely to have heart attacks than women of average height, while tall women have the fewest heart attacks. An insurance group reports that heavier cars have fewer deaths per 100,000 vehicles than do lighter cars. These and many other statistical studies look at the relationship between two variables.

slide3

CAUTION: Statistical relationships are __________, not ______.They allow individual exceptions. For example, although smokers, on average, die younger than nonsmokers, some people live to 90 while smoking three packs a day.

rules

tendencies

slide4

To understand a statistical relationship between two variables, we measure both variables on the same individual. When analyzing a relationship between two variables, we must examine other variables as well. Name two variables that could affect the heart attack study above.

weight, exersize, stress, heredity

slide5

Researchers need to eliminate the effect of these other variables. One of our main themes is that the relationship between two variables can be strongly influenced by other variables lurking in the background.

slide6

In chapter 3, we will focus on relationships between quantitative variables. Categorical variables will be examined in chapter 4. Quite often, you want to determine if one of the variables helps explain or even causes changes in the other.

slide9
Explanatory variables are sometimes called independent variables and response variables are sometimes called dependent variables.
slide11

Alcohol has many effects on the body. One effect is a drop in body temperature. To study this effect, researchers give several different amount of alcohol to mice, then measure the change in each mouse’s body temperature in the 15 minutes after taking the alcohol.Explanatory: Response:

amount of alcohol consumed

change in body temperature

slide12

Jim wants to know how the mean 2005 SAT Math and Verbal scores in the 50 states are related to each other. He wants to determine if he can predict a state’s mean SAT Math score if he knows the mean SAT Verbal score.Explanatory:Response:

mean SAT verbal score

mean SAT math score

slide13

Note that in first scenario alcohol actually causes a change in body temperature. There is no cause-and-effect relationship between SAT Verbal and Math scores.

slide14

Caution: Calling one variable explanatory and the other responsive doesn’t necessarily mean that changes in one causechanges in the other.

slide15

The most effective way to display the relationship between two quantitative variables is with a scatterplot. To draw a scatterplot by hand: Plot the explanatory variable, if there is one, on the __________ ( __ ) axis of a scatterplot. If there is no explanatory-response distinction, either variable can go on the horizontal axis. Be sure to _______ and _______ both axes. The intervals on each axis must be uniform for that axis; and adopt a scale that uses the whole grid and allows the details to be easily seen.

horizontal X

label

scale

slide16
Two variables are positively associatedwhen above average values tend to occur together on both variables.
slide17
Two variables are negatively associated when above average values on one variable tend to occur with below average values on the other.
slide18

When describing the overall pattern of a scatterplot you must address 3 key areas:direction (i.e.__________________________), form (i.e. ______________) andstrength (i.e ____________________________________)

positive or negative association

linear or curved

how closely do the points follow the form

slide19

Also note unusual aspects such as clusters of points or points that lie far outside the pattern.Points that lie far away from all the others in the vertical direction are called ________Points hat lie far away from the others in the horizontal direction are ________________

example 2 interpret the scatterplot to the right direction form strength outliers
Example 2: Interpret the scatterplot to the right:Direction:Form: Strength:Outliers:

negative association

slightly curved

fairly strong

Possible outlier at (20, 510)

to add a categorical variable to a scatterplot use a different color or symbol for each category
To add a categorical variable to a scatterplot, use a different color or symbol for each category.
slide23

Scatterplots on the TI 83/84: 1. Put the data into two lists 2. STATPLOT (2ndfunc. of Y=) 3. Make sure all but the first are turned OFF 4. Turn plot1 ON and highlight the first graph and press ENTER 5. Xlistis the explanatory variable and Ylist is theresponse variable 6. Choose the “marker” you wish to use 7. Press GRAPH and ZOOM 9 for appropriate window

slide24

Example: How does the percent of adult birds in a colony from one year that return to nest the following year, affect the number of new birds that join the colony? Here are data for 13 colonies of sparrowhawks. Construct a scatterplot and describe what you see.% returning: 74 66 81 52 73 62 52 45 62 46 60 46 38# new birds: 5 6 8 11 12 15 16 17 18 18 19 20 20