Regression Lines & Residuals

In the regression line to the left, what does "y-hat" represent?

Extrapolation is the use of the regression line for prediction (a)   of the interval of values used to obtain the line.

A residual is the difference between an ​ (a)   ​ value and it's ​ (b)   value.

What does it mean when a residual is negative?

The equation of the regression in the previous problem for predicting y = wait time from x = duration of previous eruption is $$y^{\wedge}=33.35\ +\ 13.29x$$

In one cycle, it took 62 minutes between eruptions, and the duration of the previous eruption was 2 minutes. Calculate the residual for this cycle.

The scatterplot shows the relationship between temperature in degrees Fahrenheit (x) and chirps per minute (y) for the striped ground cricket. The equation of the regression line is given below. Predict the cricket chirp rate when the temperature is $$82\degree F$$ . Round your answer to the nearest chirp.

$$y^{\wedge}=-0.31+0.212x$$

In the previous problem, the equation of the regression line for predicting y = chirps per minute from x = temperature in degrees Fahrenheit is $$y^{\wedge}=-0.31\ +\ 0.212x$$

One observation in these data measured 16.2 chirps per minute at $$83.3\degree F$$ . Calculate the residual for this observation.

The scatterplot shows the relationship between the height of a student (x) and the number of steps (y) required to walk the length of a school hallway. The equation of the regression line relating these variables is given below.

$$y^{\wedge}=113.6-0.921x$$

Predict the number of steps for a student that is 63 inches tall. Round your answer to the nearest tenth.

In the previous problem, the equation of the regression line for predicting y = number of steps required to walk the length of a school hallway from x = the height of a student (in inches) is $$y^{\wedge}=113.6-0.921x$$

One student who was 67 inches tall took 46 steps to walk the length of the hallway. Calculate the residual for this student. Round your answer to the nearest tenth.