Quiz about Regression Lines & Residuals

Question 1

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

Accepted Answer

The predicted value

Answer

The slope

Answer

The y-intercept

Answer

The residual

Question 2

What does it mean when a residual is negative?

Accepted Answer

The actual value is less than the predicted value

Answer

The actual value is more than the predicted value

Answer

The actual value is equal to the predicted value

Question 3

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.

Accepted Answer

$$2.07$$

Answer

$$-795.33$$

Answer

$$35.42$$

Answer

$$-2.07$$

Question 4

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.

Accepted Answer

$$-1.15$$

Answer

$$17.35$$

Answer

$$17.6$$

Answer

$$1.15$$

Question 5

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.

Accepted Answer

$$15.1$$

Answer

$$61.7$$

Answer

$$-15.1$$

Answer

$$51.9$$

Question 6

In the previous problem, you were given the regression line equation $$y^{\wedge}=28.17+0.2143x$$ where x represented the height (in feet) of a roller coaster and y represented the maximum speed of the roller coaster.

Calculate the residual for the roller coaster the Iron Shark, which has a height of 100 feet and a top speed of 52 miles per hour.

Accepted Answer

$$2.4$$

Answer

$$49.6$$

Answer

$$-2.4$$

Answer

$$100$$

Regression Lines & Residuals

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