Unit 6 Two Variable Statistics

6.1 Scatter Plots and Linear Correlation

In the previous unit, all the data points only told us one thing, either a counted or a measured value.

This unit the data points have two qualities such as:

Years of Education, Salary

Arm Span, Height

Height, Mark in Data Class

This unit is about examining trends in two variable statistic sets.

Dependent variable: a variable whose outcome depends on another variable.

Independent variable: a variable that affects the value of another variable.

Scatter Plot: the graphical result of a two variable relationship.

Linear Correlation: when changes in one variable are in proportion to the change in another variable.

If both variables are increasing at a similar rate the relationship has a positive linear correlation. If the dependent decreases as the independent increases, the relationship has a negative linear correlation.

Line of Best Fit: the straight line that passes as close as possible to all points in the scatter plot.

Ex 1 What kind of relationship is demonstrated by the following scatter plots? (p.160)

Observing a scatter plot on its own can tell you anecdotal evidence about the line of best fit. To prove anything about the data you need to discuss the covariance-then develop the correlation coefficient.

Covariance Formula:

It represents the mean of the products of the deviations of two variables.

This is a required formula in the development of the correlation coefficient.

The Correlation Coefficient: . This formula always gives you a number between -1 and 1 and tells how well the data clusters around the line of best fit. The closer to -1 or 1 the stronger your relationship is. (p.163)

When describing a linear correlation, be sure to use a descriptor along with positive/negative.

There is a way to calculate the correlation coefficient without using the standard deviation, it ain’t pretty, but it works:

Ex 2 A farmer wants to determine whether there is a relationship between the temperature during the growing season and the size of his wheat crop.(p.164)

(a) Draw a scatter plot on the graphing calculator.

(b) Calculate the correlation coefficient.

(c) What can the farmer conclude about the relationship between the mean temperatures during the growing season and the wheat yields on his farm?

p. 168# 1-3, 5a,6