Outliers · Exercise 9

In Table 12.31, the height (sidewalk to roof) of notable tall buildings in America is compared with the number of stories of the building (beginning at street level).

$$\begin{array}{cc}\text{Height (in feet)}& \text{Stories}\\ \text{1,050}& \text{57}\\ \text{428}& \text{28}\\ \text{362}& \text{26}\\ \text{529}& \text{40}\\ \text{790}& \text{60}\\ \text{401}& \text{22}\\ \text{380}& \text{38}\\ \text{1,454}& \text{110}\\ \text{1,127}& \text{100}\\ \text{700}& \text{46}\end{array}$$

(a) Using stories as the independent variable and height as the dependent variable, make a scatter plot of the data.
(b) Does it appear from inspection that there is a relationship between the variables?
(c) Calculate the least-squares line. Put the equation in the form ŷ = a + bx.
(d) Find the correlation coefficient. Is it significant?
(e) Find the estimated heights for a building that has 32 stories and for a building that has 94 stories.
(f) Based on the data in, is there a linear relationship between the number of stories in tall buildings and the height of the buildings?
(g) Are there any outliers in the data? If so, which point(s)?
(h) What is the estimated height of a building with six stories? Does the least-squares line give an accurate estimate of height? Explain why or why not.
(i) Based on the least-squares line, adding an extra story is predicted to add about how many feet to a building?
(j) What is the slope of the least-squares (best-fit) line? Interpret the slope.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §12.5 Outliers · Exercise 9