Question

ones. here is a scatterplot of x = height (in feet) versus y = maximum speed (in miles per hour) for nine roller coasters that opened in 2012. the equation of the regression line for this relationship is $hat{y}=28.17 + 0.2143x$. b) does the value of the y - intercept have meaning in this context? if so, interpret the y - intercept. if not, explain why. yes, what the height of the roller coaster is at c) calculate and interpret the residual for the iron shark, which has a maximum height of 100 feet and a top speed of 52 miles per hour.

Explanation:

Step1: Recall the concept of y - intercept

The regression line equation is $\hat{y}=28.17 + 0.2143x$. The y - intercept is the value of $\hat{y}$ when $x = 0$. In this context, $x$ is the height of the roller - coaster in feet. A height of $x = 0$ feet is not a realistic situation for a roller - coaster. So the y - intercept has no meaning in this context.

Step2: Calculate the predicted value for the Iron Shark

Substitute $x = 100$ into the regression line equation $\hat{y}=28.17+0.2143x$.
$\hat{y}=28.17 + 0.2143\times100=28.17 + 21.43=49.6$

Step3: Calculate the residual

The residual $e=y-\hat{y}$. Given $y = 52$ (actual speed) and $\hat{y}=49.6$ (predicted speed).
$e=52 - 49.6 = 2.4$
The residual of 2.4 means that the actual maximum speed of the Iron Shark is 2.4 miles per hour higher than the speed predicted by the regression line.

Answer:

b) No, a roller - coaster with a height of 0 feet is not a realistic situation, so the y - intercept has no meaning in this context.
c) The residual is 2.4. It means the actual maximum speed of the Iron Shark is 2.4 miles per hour higher than the speed predicted by the regression line.