Warm-Up A trucking company determines that its fleet of trucks averages a mean of 12.4 miles per gallon with a standard deviation of 1.2 miles per gallon on cross-country hauls. What proportion of the trips average fewer than 10 miles per gallon? 0.0082 0.0228 0.4772 0.5228 0.9772

Describing Relationships Section 3.1 Scatterplots and Correlation

Variables A response variable measures an outcome of a study. An explanatory variable may help explain or influence changes in a response variable. Example: amount of rain – explanatory grass growth – response Example: test grades – time spent studying –

Scatterplots The most useful graph for displaying relationships between two quantitative variables is a scatterplot. A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point in the graph.

How to make a scatterplot: Decide which variable should go on each axis (dependent vs. independent) X-axis is your independent data (explanatory variable) Y-axis is your dependent data because it “depends” on what you put in for x! (response variable) Label and scale your axes Plot individual data points

Make a quick scatterplot Body Weight (lb) 120 187 109 103 131 165 158 116 Backpack Weight (lb) 26 30 24 29 35 31 28

Interpreting Scatterplots As in any graph of data, look for the overall pattern and for striking departures from that pattern. You can describe the overall pattern of a scatterplot by the direction, form, and strength of the relationship. An important kind of departure is an outlier, an individual value that falls outside the overall pattern of the relationship.

Describing Scatterplots Direction – does it have a positive or negative correlation? Form – is it linear, quadratic, exponential? We really care about linear or not linear. Strength – how closely do the points follow a clear form? FODS (Form, Outlier, Direction, Strength)

Correlation

The correlation r measures the direction and strength of the linear relationship between two quantitative variables. (always a number between -1 and 1)

Facts about correlation Correlation makes no distinction between explanatory and response variables. The correlation r itself has no unit of measurement. It is just a number! Correlation requires that both variables be quantitative. Correlation does not describe curved relationships, no matter how strong the relationship is. Like the mean and standard deviation, the correlation is not resistant. Correlation is not a complete summary of two-variable data. You should also give the mean and standard deviation of x and y.

ALL Homework’s Up Front Page 158  (1-13, 15-17) Page 161  (18-19, 22-23, 25-32) Page 192  (47-66) Page 191  (35-42, 44-46)