![]() What you may see in a pattern of dots I may interpret differently (it’s like looking at clouds patterns in the sky). There still remains some subjectivity when describing the relationship between two data values from a scatterplot. Measuring the Strength of a Linear Relationship Common sense suggests that there is not a relationship, linear or otherwise, between a person’s IQ and his or her shoe size. Thus, the scatter plot would have a positive slope.ĭ. The more you push on the gas pedal, the faster the car will go. Thus, the scatter plot would have a negative slope.Ĭ. As the number of miles on the odometer of a used car increases, the price usually decreases. Thus, the scatter plot would have a positive slope.ī. As the number of hours you study for an exam increases, the score you receive on that exam is usually higher. The pressure on a gas pedal and the speed of the carĪ. The price of a used car and the number of miles on the odometerĬ. The number of hours you study for an exam and the score you make on that examī. This relationship is more quadratic in nature, with an example shown in the left image.Įxample: Determining Whether a Scatter Plot Would Follow a Straight-Line Patternĭetermine whether the points in a scatter plot for the two variables are likely to have a positive slope, negative slope, or not follow a straight-line pattern.Ī. An excellent example of a nonlinear data set is the relationship between the speed you drive your car and the corresponding gas mileage. Some data exhibits a nonlinear (or curved) relationship. For used cars, there is a negative association between the age of the car and the selling price.From a scatterplot of college students, there is a positive association between verbal SAT score and GPA.Some examples of data with a linear relationship are: This type of relationship between two variables is called a negative linear relationship. A negative slope indicates that as the values of one variable increase, the values of the other variable decrease. This type of relationship between two variables is called a positive linear relationship. A positive slope indicates that as the values of one variable increase, so do the values of the other variable. When the points in a scatter plot do roughly follow a straight line, the direction of the pattern tells how the variables respond to each other. Likewise, two variables have a negative association if above-average values of one variable tend to accompany below-average values of the other variable, and vice versa. We say two variables have a positive association if above-average values of one variable tend to accompany above-average values of the other variable, and below-average values tend to occur together. Some relationships are such that the points of a scatterplot tend to fall along a more-or-less straight line. Two variables have a linear relationship in a scatter plot when the two variables roughly follow a straight-line pattern. This is a process very similar to describing distributions! You can describe the pattern by form, direction, and strength of the relationship, and you can identify points that do not follow the overall pattern (outliers). Once you have a scatterplot, it can be used to identify an overall pattern and deviations from this pattern. It’s now quite clear that as the number of absences increases, the final course grade decreases. A scatteplot created in Excel looks like: Typically we rely on technology to create the scatterplot for us. Plot the 10 points on the xy-axes, using the points (0, 89.2) (1, 86.4), and so on. In this case, the professor hopes that the number of a student’s absences will offer some explanation of his or her final course grade. Identifying the relationship between the two data values from a table is difficult, so we create a scatterplot. The data shown were collected from a sample of students in a general education course. With a scatterplot, each individual in the data set is represented by a single point ( x, y) in the xy-plane.Įxample (taken from Fundamentals of Statistics, by Sullivan):Ī professor at a large midwestern university wanted to study the relationship between the number of class absences a student has in a given semester and that student’s final course grade. If a distinction exists in the two variables being studied, plot the explanatory variable (X) on the horizontal scale, and plot the response variable (Y) on the vertical scale. The most useful graph to show the relationship between two quantitative variables is the scatter diagram.
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