Unit 6 describing data/scatter plots Wednesday 8/23/2017 Unit 6 describing data/scatter plots

Scatter plots Recall: Coordinate plane- A two-dimensional surface on which points are plotted and located by their x and y coordinates (x,y). This point is made by moving horizontally along the x-axis using the first number in the coordinate pair and then using the second number moving vertically along the y-axis. Equation of a line- y=mx+b, where x and y are variables that will give you coordinates along the line, and m is the slope of the line, and b is where the line crosses the y-axis.

Scatter plots A scatter plot is a graph of plotted points that shows a relationship between two sets of quantitative data (referred to as bivariate data). Scatter plots are composed of "dots" (points) on a set of coordinate axes. Do NOT connect the dots! Scatter plots are a popular and effective way of graphing data to display patterns, trends, relationships and an occasional extraordinary value located apart from the other values. (outliers)

Scatter plots Example: Does studying for that Final Exam really help your score? Does one event really affect the other? The scatter plot at the right appears to show that the longer students studied, the higher their examination scores. According to this survey of 15 students studying for the same examination, it appears that the answer to our initial question is "yes", studying does affect your score. At least, the answer is "yes", for this particular group of students.

Scatter plots Notice how the data in the graph resembles a straight line rising from left to right. When working with scatter plots, if is often useful to represent the data with the equation of a straight line, called a "line of best fit", or a "trend" line. Such a line may pass through some of the points, none of the points, or all of the points on the scatter plot.

Scatter plots: Line of Best Fit Predicting: - If you are looking for values that fall within the plotted values, you are interpolating. - If you are looking for values that fall outside the plotted values, you are extrapolating.  Be careful when extrapolating.  The further away from the plotted values you go, the less reliable is your prediction.

linear function y = mx + b Does the plotted data resemble a straight line? • the slope may be either positive or negative. • linear associations are the most popular because they are easy to read and interpret. • "line of best fit"

quadratic function y = ax2 + bx + c Does the plotted data resemble a parabola, or part of a parabola? • the shape may open upward or downward. • "quadratic of best fit"

exponential function y = abx + c Does the plotted data resemble an exponential curve? • the curve will either rise or fall. • the curve will not "turn around" like a parabola. • "exponential of best fit"

Shapes of functions Beware: It may not always be obvious from looking at the scatter plot which shape (curve) will be the best fit. Some situations may require more investigation before deciding upon a possible shape (curve), and some situations may not be modeled by any of these shapes (curves).