Question

In: Statistics and Probability

The height (sidewalk to roof) of notable tall buildings in America is compared to the number...

The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level).

Height (in feet) Stories
1050 58
428 27
362 26
529 40
790 60
401 22
380 38
1454 110
1127 100
700 46

Calculate the least squares line. Put the equation in the form of:

ŷ = a + bx

Find the correlation coefficient r.

Find the estimated height for 34 stories. (Use your equation from part (c). Round your answer to one decimal place.)
ft

Find the estimated height for 93 stories

What is the estimated height of a building with 7 stories

Based on the least squares line, adding an extra story adds about how many feet to a building?

What is the slope of the least squares (best-fit) line?

Solutions

Expert Solution

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.946181613
R Square 0.895259644
Adjusted R Square 0.882167099
Standard Error 129.7489819
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 1151152.514 1151152.514 68.37934695 3.43853E-05
Residual 8 134678.3864 16834.7983
Total 9 1285830.9
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 102.9563554 85.3788132 1.205877097 0.262316127 -93.92754069 299.8402516 -93.92754069 299.8402516
Stories 11.74845625 1.420752175 8.269180549 3.43853E-05 8.472195865 15.02471664 8.472195865 15.02471664

the least squares line ŷ = a + bx

ŷ = 102.956 + 11.748 * x

Height (in feet) = 102.956 + 11.748 * Stories

the correlation coefficient r = 0.95 = 95%

the estimated height for 34 stories

Height (in feet) = 102.956 + 11.748 * Stories

= 102.956 + 11.748 * 34

= 502.388 = 502.4

the estimated height for 93 stories

Height (in feet) = 102.956 + 11.748 * Stories

= 102.956 + 11.748 * 93

= 1195.5

the estimated height of a building with 7 stories

Height (in feet) = 102.956 + 11.748 * Stories

= 102.956 + 11.748 * 7

= 185.2

Based on the least squares line, adding an extra story adds about 11.748 feet to a building

the slope of the least squares (best-fit) line = 11.748


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