The Basics (Plotting & Reading)
In an ordered pair $(x, y)$, this variable is typically used for the "independent" data and plotted on the horizontal axis.
What is the x-variable?
If the $y$-values decrease as the $x$-values increase, the scatter plot is said to have this type of association.
What is a negative correlation?
This is a straight line drawn through a scatter plot to summarize the relationship between the two sets of data.
What is a line of best fit (or trend line)?
If the data points are packed very tightly around the line of best fit, the correlation is described as being this.
What is strong?
If a scatter plot shows a negative correlation between "Distance from Home" and "Signal Strength," what happens to your signal as you drive away?
What is it gets weaker
This is the specific term for a data point that is located far away from the rest of the "cloud" of points.
What is an outlier?
A scatter plot showing the relationship between "Student Shoe Size" and "Test Scores" would likely show this type of correlation.
What is no correlation (or zero correlation)?
When using a line of best fit, you are making a prediction. If you predict a value outside the range of your known data points, it is called this.
What is extrapolation?
This term refers to a distinct group of points that are located close together, separate from the rest of the data.
What is a cluster?
A scientist plots the height of a plant over 10 days. Would you expect the correlation to be positive, negative, or none?
What is positive?
When looking at a table of data, this is the name of the variable you choose or control (the $x$).
What is the independent variable?
This term describes a relationship where the points follow a curved path like a "U" or a "rainbow" shape.
What is a non-linear association?
In the equation $y = mx + b$, which letter represents the slope of the line of best fit?
What is m?
If two variables increase together, but the points are spread out and only vaguely look like a line, the correlation is described as this.
What is weak positive?
You are analyzing a scatter plot of Temperature ($x$) vs. Hot Cocoa Sales ($y$). The line of best fit is $y = -2x + 150$.
Calculate the predicted sales if the temperature is 70 degrees.
If the actual sales at 70 degrees were 5 units, what is the difference between the prediction and the actual value?
$10 ($-2 \times 70 = -140$; $140 + 150 = 10$).
$5 (The "residual" or error is $10 - 5 = 5$).
If a scatter plot has 50 points and 1 point is at $(100, 2)$ while the rest are near $(10, 10)$, that single point is called this.
What is an outlier?
If every single point on a scatter plot falls exactly on the line of best fit, we call this a _________ correlation.
What is perfect?
To find the line of best fit accurately, mathematicians often use the "Least _______" method.
What is Squares?
True or False: A line of best fit must pass through at least two of the actual data points on the graph.
What is False? (It represents the trend, but doesn't have to touch any specific point).
how tall is tayton
67 foot tall
On a scatter plot comparing "Ice Cream Sales" to "Outside Temperature," this variable would be considered the dependent variable.
What are Ice Cream Sales?
This term describes a pattern where the points roughly follow a straight line, as opposed to a curve.
What is a linear association?
If a line of best fit is $y = 2x + 5$, this specific number represents the "starting value" or where the line crosses the vertical axis.
What is the y-intercept?
True or False: If a scatter plot shows a strong positive correlation between two variables, it means that one variable causes the other to happen.
What is False?
In a study of "Hours of Video Games" vs. "Hours of Sleep," the data shows a strong negative association. If a student plays 5 more hours of games, what happens to their sleep?
What is it decreases?