AP Statistics Least-Squares Regression and Residuals Quiz: 10 Questions with Explanations

A the predicted y increases by 4 for each one-unit increase in xB y increases by exactly 4 for every unit of xC when y is 0, x is 4D x increases by 4 for every unit of y

The slope is a predicted change per unit of x. Actual values vary around the line.

A predicted y minus actual yB the slope times xC actual y minus predicted yD the correlation squared

Residual = y – y-hat. A positive residual means the point is above the line.

A A linear model is appropriateB A curved model is neededC There are no residualsD The slope is zero

Random scatter around zero without a pattern supports a linear model.

A A linear model is fineB The relationship is not linearC The data are categoricalD r equals 1

A clear U shape in the residuals means a curved model would fit better.

A 75% of the variation in y is explained by the linear relationship with xB 75% of the points lie on the lineC the slope is 0.75D the correlation is 0.75

r squared is the proportion of variation explained, not the number of points on the line.

A safe because the line is straightB extrapolation and unreliableC interpolationD always correct

Age 20 is far outside the data range, so there is no evidence the pattern continues.

A the originB the point (x-bar, y-bar)C the first data pointD the point with the largest residual

Because a = y-bar – b x-bar, the line goes through the point of means.

A 0.2B 0.5C 1.25D 5

b = r sy/sx = 0.5(10/4) = 1.25. Using sx/sy gives 0.2.

A the slopeB the explained variationC the correlationD the typical size of the prediction error

s is the typical distance of actual y values from the predicted values.

A a residualB a lurking variableC the meanD influential

Points with extreme x values that substantially change the line are influential.