Here are some examples (“≈” symbol means approximately equal to): A correlation coefficient of or near 0 means there’s no connection at all between the two variables. For example, there seems to be a strong correlation between shark attacks and ice cream sales of course shark attacks do not cause people to buy ice cream, but in hot weather, both shark attacks and people buying ice cream are more likely to occur.Īgain, correlation can be thought of as the degree in which two things relate to each other, and the correlation coefficients are anywhere from –1 (strong negative correlation) to 1 (strong positive correlation). Note that a positive correlation doesn’t necessarily mean that the effect of one variable causes the effect on the other variable (a causal relationship, or causation) there may be a third effect that causes both of the variables to make the same type of changes. Since the trend is that when the $ x$-values go up, the $ y$-values also go up, we call this a positive correlation, and the correlation coefficient is positive. Thus, if we were to try to fit a line through the points, which is a statistical calculation that finds the “closest” line to the points, it would have a positive slope. Notice from the scatter plot above, generally speaking, the friends who study more per week have higher GPAs. A scatter plot is just a graph of the $ x$-points (number of hours studying each week) and the $ y$-points (grade point average): To make more sense of the data, let’s first order it by the number of hours of studying: Friend It seems like the two variables would be related, but suppose you survey some of your friends to see what a graph would look like: As an example of interpreting sets of data, we may want to see if there is some sort of connection between two sets of data, such as the number of hours studied per week versus grade point average. In the real world, there are always sets of data that need to be interpreted. These include Scatter Plots, Correlation, and Regression, including how to use the Graphing Calculator. Usually around the time that you are beginning “Algebra II” you’ll have another lesson on a little more advanced Statistics than you had earlier (in the Introduction to Statistics and Probability section). Using Graphing Calculator to Get Line of Best Fit
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