Question

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	57
428	28
362	26
529	40
790	60
401	22
380	38
1454	110
1127	100
700	46

Based on the least squares line, adding an extra story adds about how many feet to a building? (Round your answer to three decimal places.)
ft______________

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Height (in feet)
Independent Variable: Stories
Height (in feet) = 102.42868 + 11.758469 Stories
Sample size: 10
R (correlation coefficient) = 0.94357547
R-sq = 0.89033468
Estimate of error standard deviation: 132.76439

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	102.42868	87.606133	? 0	8	1.1691953	0.276
Slope	11.758469	1.4590286	? 0	8	8.059108	<0.0001

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	1144819.8	1144819.8	64.949221	<0.0001
Error	8	141011.06	17626.383
Total	9	1285830.9

Hence,

Slope = 11.758

So,

Adding an extra story adds about 11.758 feet to a building.