Vocabulary
A _____ _____ measures an outcome of a study. (located on the y-axis)
Response variable
The value of correlation is always between ___ and ___.
(-1, 1)
What is the equation for the LSRL?
y-hat = a + b(x)
Why is it important to use y-hat (predicted) in an LSRL and not assume it is the actual value?
The LSRL is an estimated line of fit, it is not always accurate. We use residuals to highlight how accurate a LSRL is.
What is the standard deviation of residuals (s)?
The approximate size of a typical prediction error (residual).
A _____ _____ may help explain or predict changes in a response variable. (located on the x-axis)
Explanatory variable
Use DOFS to describe this scatter plot. r=-0.99
D: Negative association
O: None
F: Linear
S: Strong
y-hat = 100 + 40(x)
What is the slope of the regression line? Interpret this value in context.
As the x-value increases by 1 unit, the predicted y-value increases by 40 units.
What is a residual?
The difference between an observed value of the response variable and the value predicted by the regression line.
What is the coefficient of determination (r^2)?
The fraction of the variation in the values of y that is accounted for by the LSRL.
What kind of graph shows the relationship between two quantitative variables measured on the same individuals?
Scatter plot
If women always married men who were 2 years older than themselves, what would be the correlation between the ages of the husband and wife be?
1
y-hat = 100 + 40(x)
What is the y-intercept of the regression line? Interpret this value in context.
The predicted y-value is 100 when x is equal to 0.
True or false: Residual = Actual value - Predicted value
True
When using the LSRL among an x and y-hat relationship, we are typically off by 1.24 units.
88% of variation in y is accounted by the LSRL.
What are the 4 main features when describing a scatter plot?
Direction, outliers, form, strength
What is the unit for correlation?
None, there is no unit!
True or false: the hat in y-hat for a LSRL represents the actual value when x equals a number.
False
The actual price of a used truck with 70,583 miles driven is $21,994. If the estimated price is $26,759, what is the residual? Did we overestimate or underestimate the price?
The residual is -$4,765. We overestimated the price of the used truck by $4,765.
True or false: the square root of r^2 equals the correlation.
True
A ____ is a line that describes how a response variable y changes as an explanatory variable x changes.
LSRL (Least Squares Regression Line)
True or false: correlation is resistant against outliers.
False
is the use of an LSRL for a prediction far outside the interval of values of the explanatory variable x to obtain the line. Such predictions are not accurate.
Extrapolation
If the actual y-value is greater than the predicted y-value, did we overestimate or underestimate the value?
We would have underestimated the y-value.
If r^2 = 0.5783, what is the correlation?