Warm up In a population of 10 th grade girls, the mean height is 65 in. If 15% of the population is...

Warm up

In a population of 10th grade girls, the mean height is 65 in. If 15% of the population is under 61 inches tall, what is the standard deviation?

3.1 :: Scatterplots and Correlation

explanatory variable

may help explain or influence changes in a response variable

(the “x”)

response variable

measures an outcome of a study

(the “y”)

What are the explanatory and response variables?

How does drinking beer affect the level of alcohol in our blood? The legal limit for driving in all states is 0.08%. In a study, adult volunteers drank different numbers of cans of beer. Thirty minutes later, a police officer measured their blood alcohol levels.

Julie asks, “can I predict a state’s mean SAT Math score if I know its mean SAT Critical Reading score?”

Jim wants to know how the mean SAT Math and Critical Reading scores this year in the 50 states are related to each other.

For each student, identify the explanatory variable and the response variable if possible.

What are the explanatory and response variables?

Describe the scatterplot- we are looking at overall patterns

SOCS vs DOFS➔SOCS is for univariate data

◆ Shape

◆ Outliers/Unusual things

◆ Center

◆ Spread

➔DOFS is for bivariate data

◆ Direction

◆ Outliers

◆ Form

◆ Strength

Heavy Backpacks

9th graders go on a backpacking trip each fall. Students are divided into hiking groups of size 8 by selecting names from a hat. Before leaving, students and their backpacks are weighed.

Describe the Scatterplot - DOFS

Correlation

POSITIVE CORRELATION NEGATIVE CORRELATION

Correlation

Correlation coefficient “r”

r - The Correlation Coefficient

If two things are highly correlated, does that mean that one causes the other????

http://www.tylervigen.com/spurious-correlations


http://www.tylervigen.com/spurious-correlations

SOME FACTS ABOUT “r”

• no units

• only measures a linear relationship

• is not resistant to outliers

• changing the units of your explanatory or response variable does not affect r

• r can only describe the correlation between quantitative variables!


Put it all together…

What would happen to the data set if we removed the possible outlier…

Answer:

The linear correlation would weaken if we removed the outlier.

However, sometimes a correlation is strengthened by removing an outlier.

Warm up In a population of 10 th grade girls, the mean height is 65 in. If 15% of the population is...

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