Correlation and Association Scatterplots Correlation and Association

Correlation and Association T. Serino Correlation and Association Objectives: 1. Students will be able to identify positive and negative association between variables. 2. Students will use the correlation coefficient to describe the strength and direction of a correlation.

Correlation and Association T. Serino Correlation and Association Correlation (r): A “unitless” measure describing a linear relationship between quantitative variables. The correlation coefficient r describes the strength and direction of the scatterplot.

Correlation and Association T. Serino Correlation and Association The Correlation of a set of data is always between -1 and 1 r = -1 Perfectly straight line with negative slope. r = 1 Perfectly straight line with positive slope. r = 0 Complete Scatter. No Relationship between the variables.

Correlation and Association T. Serino Correlation and Association The direction of the correlation is either positive or negative. Positive Correlation: The trend line through the data will have positive slope. (as x increases, y also increases) These graphs all have a positive correlation. The correlation coefficient, r will be positive.

Correlation and Association T. Serino Correlation and Association The direction of the correlation is either positive or negative. Negative Correlation: The trend line through the data will have negative slope. (as x increases, y decreases) These graphs all have a negative correlation. The correlation coefficient, r will be negative.

Correlation and Association T. Serino Correlation and Association No Correlation: When the variables are not related, we can’t draw a trend line, because there is no linear trend in the data. None of these graphs have any correlation. The correlation coefficient, r will be zero.

Correlation and Association T. Serino Correlation and Association The strength of the correlation is determined by the amount of scatter. Very little scatter will give a correlation close to 1 or -1. A lot of scatter will give a correlation close to 0. Weak Positive Correlation Perfect Positive Correlation Strong Positive Correlation Very little scatter. (r close to 1) A lot of scatter. (r close to 0) No scatter. (r = 1)

Correlation and Association T. Serino Correlation and Association The strength of the correlation is determined by the amount of scatter. Very little scatter will give a correlation close to 1 or -1. A lot of scatter will give a correlation close to 0. Weak Negative Correlation Strong Negative Correlation Perfect Negative Correlation A lot of scatter. (r close to 0) Very little scatter. (r close to -1) No scatter. (r = -1)

Correlation and Association T. Serino Correlation and Association Try this: Describe the strength (strong or weak) and direction (positive or negative) of the following scatterplots. (If there is no correlation, state, “no correlation”) 1 2 3 4 5 6

Correlation and Association T. Serino Correlation and Association Given two variables, you can often determine the direction of the correlation by comparing the direction of each variable. Positive direction: As one variable increases, the other will also increase. (The two variables move in the same direction.) Negative direction: As one variable increases, the other will decrease. (The two variables move in the opposite direction.)

Correlation and Association T. Serino Correlation and Association Example: As the temperature becomes warmer, June is able to spend more time outside. This statement is talking about two variables: temperature, and length of time June spends outside. Do these two variables have positive correlation, negative correlation, or no correlation? As the temperature increases, June’s time outside also increases. This is a positive correlation.

Correlation and Association T. Serino Correlation and Association Example: As the number of wolves in the forest increases, the number of deer in the forest decreases. What are the two variables being discussed here? Do they have positive correlation, negative correlation, or no correlation? The variables are number of wolves and number of deer. As the number of wolves increase, the number of deer decrease. This is a negative correlation.

Correlation and Association T. Serino Correlation and Association Example: Every day the weatherwoman predicts the high temperature for the day. Every day Loren records the high temperature of the day according to his thermometer. As far as Loren can tell, the weatherwoman's prediction has nothing to do with the actual high temperature for the day. What are the two variables being discussed here? Do they have positive correlation, negative correlation, or no correlation? The variables are the predicted high temperature (from the weatherwoman) and the actual high temperature (measured by Loren). Because the two variables seem to have no relationship, there is No Correlation.

Correlation and Association T. Serino Correlation and Association Try this: Determine if there is a positive correlation, a negative correlation, or no correlation. Amount of free time vs. Number of college classes taken Number of gallons of heating oil consumed vs. Average Daily temperature Air pollution levels vs. Number of cars on the road Shoe size vs. Grade point average

Correlation and Association T. Serino Correlation and Association Association: A more vague term used to describe a relationship between quantitative variables. The difference between correlation and association is that correlation shows a linear relationship whereas association does not need to be linear.

Correlation and Association T. Serino Correlation and Association Ex) Describe the correlation or association. No Correlation Weak Positive Correlation Strong Negative Correlation Strong Association No Correlation, because the relationship is not linear. This point seems to be an outlier.

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