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). Stories (x-value) Height In feet (y-value) 57 1,050 28 428 26 362 40 529 60 790 22 401 38 380 110 1,454 100 1,127 46 700 Use the regression analysis to answer the following questions.

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

Are there any outliers in the data? If so, which point(s)? You must explain your answer using the definition defined by our book using standard error.

Answer 1

Sol:

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.

Using the Scatter Plot , It is observed that there are outliers in the given data as two of the dotted points lie a bit away from the straight line or linear trendline. The outliers in form of (x,y) are (100,1100) and (110,1400).