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AP Statistics BVD Chapter 7 and 8: Scatterplots, Associations, Correlation, and Linear Regression
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Key Concepts:
Terms in this set (24)
scatterplots
a graph that shows the relationship between two quantitative variables measured on the same case.
direction, form, and strength
association between to variables has these three characteristics
positive direction
as one variable increases, the second variable increases
negative direction
as one variable increases the other decreases
form
the shape we see in a scatterplot, examples are linear, quadratic, exponential
strength
the amount of scatter shown in a scatterplot from the underlying relationship
outlier
a point that does not fit the overall pattern seen in a scatterplot
response variable
usually the y-variable that is also called the range, the dependent variable, or the predicted variable when using the regression model
explanatory variable
usually the x-variable that is also called the domain, the independent variable, or the predictor when using the regression model
correlation coefficient
a numerical measure of the direction and strength of a linear association
lurking variable
a variable other than x and y that SIMULTANEOUSLY affects both variable, accounting for the correlation between the two variables
model
an equation or formula that simplifies and represents reality
linear model
an equation of a line
predicted value
the value of y-hat for a given x, these are values found on the line of best-fit
residuals
the value that is the difference between data values and corresponding predicted values
least squares
specifies the unique line that minimizes the variance of the residuals or, equivalently, the sum of the squared residuals
regression to the mean
each predicted y-hat tend to be fewer standard deviation from its mean that its corresponding "x" was from its mean
regression line (Line of Best Fit)
y-hat = b-knot + b subscript one * x
slope
gives a value in "y units per x units." the rate of change
intercept
the y-hat when x = 0, also the b knot
S with subscript e
the standard deviations of the residuals
R squared
the square of the correlation coefficient, also called the coefficient of determination, this will give the fraction of variability of "y: accounted for by the least squares linear regression on x.
The Gateway Arch
630-foot monument in St. Louis in the U.S. state of Missouri. Clad in stainless steel and built in the form of an inverted, weighted catenary arch, it is the world's tallest arch
Mississippi River
is the chief river of the second-largest drainage system on the North American continent, second only to the Hudson Bay drainage system. Wikipedia
Length: 2,320 mi
Source: Lake Itasca
Mouth: Gulf of Mexico
Start: Lake Itasca
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