SOPHIA STATISTICS MILESTONE 5 FORMULAS
AND CALCULATION FLASHCARDS 2026
◉ inappropriate grouping. Answer: Combining together subgroups
that should not be combined, resulting in a weakened, or even
reversed, association.
◉ correlation. Answer: A statistic which measures the strength and
direction of the linear association between two quantitative
variables.
◉ Causation/Cause-and-Effect. Answer: A phenomenon whereby an
increase in one variable directly leads to an increase or decrease in
another variable.
◉ causality. Answer: A cause-and-effect relationship between two
variables.
◉ Best-Fit Line/Trend Line/Regression Line. Answer: A line that
closely approximates the response values for given explanatory
values when the form of the scatterplot is linear.
◉ slope. Answer: The rate of change relating the increase or
decrease in y to an increase of 1 in x.
,◉ y-intercept. Answer: The value of y when x = 0.
◉ residual. Answer: The difference between the actual value of the
response variable for a particular data point and its predicted value
from the regression line.
◉ residual plot. Answer: A scatter plot that plots Residuals vs.
explanatory variable, as opposed to response variable vs.
explanatory variable. It can be used to assess the fit of a line.
◉ Least-Squares Line. Answer: A best-fit line that is found through a
process of minimizing the sum of the squared residuals.
◉ X-bar (x with a line over it). Answer: The average x value for a
sample
◉ Y-bar (y with a line over it). Answer: The average y value for a
sample
◉ Slope of Regression Line. Answer: The amount y changes (on
average) for a one unit increase in x.
, ◉ Y-Intercept of Regression Line. Answer: The expected y value
when x = 0
◉ multiple regression. Answer: Using more than one explanatory
variable to predict the value of the response variable.
◉ extrapolation. Answer: Using the regression line to make
predictions outside the window for which the model was intended.
◉ Bar Graph. Answer: A distribution of qualitative data that displays
bars that are proportional in length to the frequency or relative
frequency of a particular data value
◉ Steps for pie chart. Answer: Step 1: Find relative frequency
Step 2: Calculate the central angle using the relative frequency.
Step 3: Create the sectors
Step 4: Add a key
◉ pie chart / circle graph. Answer: A distribution of qualitative data
that shows the relative frequency of each category as a sector of a
circle.
AND CALCULATION FLASHCARDS 2026
◉ inappropriate grouping. Answer: Combining together subgroups
that should not be combined, resulting in a weakened, or even
reversed, association.
◉ correlation. Answer: A statistic which measures the strength and
direction of the linear association between two quantitative
variables.
◉ Causation/Cause-and-Effect. Answer: A phenomenon whereby an
increase in one variable directly leads to an increase or decrease in
another variable.
◉ causality. Answer: A cause-and-effect relationship between two
variables.
◉ Best-Fit Line/Trend Line/Regression Line. Answer: A line that
closely approximates the response values for given explanatory
values when the form of the scatterplot is linear.
◉ slope. Answer: The rate of change relating the increase or
decrease in y to an increase of 1 in x.
,◉ y-intercept. Answer: The value of y when x = 0.
◉ residual. Answer: The difference between the actual value of the
response variable for a particular data point and its predicted value
from the regression line.
◉ residual plot. Answer: A scatter plot that plots Residuals vs.
explanatory variable, as opposed to response variable vs.
explanatory variable. It can be used to assess the fit of a line.
◉ Least-Squares Line. Answer: A best-fit line that is found through a
process of minimizing the sum of the squared residuals.
◉ X-bar (x with a line over it). Answer: The average x value for a
sample
◉ Y-bar (y with a line over it). Answer: The average y value for a
sample
◉ Slope of Regression Line. Answer: The amount y changes (on
average) for a one unit increase in x.
, ◉ Y-Intercept of Regression Line. Answer: The expected y value
when x = 0
◉ multiple regression. Answer: Using more than one explanatory
variable to predict the value of the response variable.
◉ extrapolation. Answer: Using the regression line to make
predictions outside the window for which the model was intended.
◉ Bar Graph. Answer: A distribution of qualitative data that displays
bars that are proportional in length to the frequency or relative
frequency of a particular data value
◉ Steps for pie chart. Answer: Step 1: Find relative frequency
Step 2: Calculate the central angle using the relative frequency.
Step 3: Create the sectors
Step 4: Add a key
◉ pie chart / circle graph. Answer: A distribution of qualitative data
that shows the relative frequency of each category as a sector of a
circle.
