In: Statistics and Probability
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?
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