11 terms

Ch 9.2: Linear Regression

regression line (line of best fit)
the line for which the sum of the squares of the residuals is a minimum
residual (di)
the difference between the observed y-value and the predicted y-value (can be positive, negative, or 0)
equation of a regression line
y(hat) = mx + b
y represents the
observed y-value for a data point
y(hat) represents the
predicted y-value (on a regression line)
y(bar) represents the
average of all y-values
x(bar) represents the
average of all x-values
the regression line always passes through point ...
x(bar), y(bar)
Given a set of data and a corresponding regression​ line, describe all values of x that provide meaningful predictions for y
Prediction values are meaningful only for​ x-values in​ (or close​ to) the range of the original data.
In order to predict​ y-values using the equation of a regression​ line, what must be true about the correlation coefficient of the​ variables?
The correlation between variables must be significant.
Is it appropriate to use a regression line to predict​ y-values for​ x-values that are not in​ (or close​ to) the range of​ x-values found in the​ data?
It is not appropriate because the regression line models the trend of the given​ data, and it is not known if the trend continues beyond the range of those data.