Handout 6 Extra Lin Reg Problems
1.) The relationship between the depth of flooding and the amount of flood damage was
examined in the paper “Significance of Location in Computing Flood Damage” (Journal
of Water Resources Planning and Management <1985>: 65-81). The following data on x
= depth of flooding (feet above first-floor level) and y = flood damage (as a percentage
of structure value) was obtained using a sample of flood insurance claims:
a.
b.
c.
d.
X 1
2
3
4
5
6
7
Y 10
14
26
28
29
41
43
X 8
9
10
11
12
13
Y 44
45
46
47
48
49
Obtain the equation of the least-squares line.
Construct a scatter plot, and draw the least-squares line on the plot. Does it look as
though a straight line provides an adequate description of the relationship between
y and x? Explain.
Predict flood damage for a structure subjected to 6.5 ft. of flooding.
Would you use the least-square line to predict flood damage when depth of flooding
is 18 ft? Explain.
2.) A number of studies have shown that lichens (certain plants composed of an alga and a
fungus) are excellent bioindicators of air pollution. The article “The Epiphytic Lichen
Hypogymnia physodes as a Bioindicator of Atmospheric Nitrogen and Sulphur
Deposition in Norway” (Environmental Monitoring and Assessment <1993>: 27-47) gives
the following data (read from graph in the paper) on x = No, wet deposition (in grams
per cubic meter) and y = lichen (% dry weigh):
X 0.05
0.10
0.11
0.12
0.31
Y 0.48
0.55
0.48
0.50
0.58
X 0.37
0.42
0.58
0.68
0.68
Y 0.52
1.02
0.86
0.86
1.00
X 0.73
0.85
0.92
Y 0.88
1.04
1.70
a. What is the equation of the least-squares regression line?
b. Predict lichen dry weight percentage for an NO, deposition of 0.5 g/m3.
3.) Athletes competing in a triathlon participated in a study described in the paper “Myoglobinemia and Endurance
Exercise” (American Journal of Sports Medicine <1984>: 113-118). The following data on finishing time x (in hours)
and myoglobin level y (in nanograms per millimeter) were read from a scatter plot in the paper:
a.
b.
c.
X
4.90
4.70
5.35
Y
1590
1550
X
5.40
5.70
6.00
Y
905
895
910
X
5.60
5.35
5.75
5.35
6.00
Y
540
540
440
380
300
1360
5.22
895
6.20
700
5.20
865
6.10
675
Obtain the equation of the least-squares line.
Interpret the value of slope
What happens if the line in part (a) is used to predict the myoglobin level for a finishing time of 8 hr?
Is this reasonable? Explain.
4.) The following data on sale price, size, and land-to-building ratio for 10 large industrial properties appeared in
the paper “Using Multiple Regression Analysis in Real Estate Appraisal” (Appraisal Journal <2002>: 424-430):
______________________________________________________________
Property
Sale Price
Size
(millions
(thousands
Of dollars)
0f sq. ft.)
1
10.6
2166
2
2.6
751
3
30.5
2422
4
1.8
224
5
20.0
3917
6
8.0
2866
7
10.0
1698
8
6.7
1046
9
5.8
1108
10
4.5
405
a.
b.
c.
d.
Land-to-Building
Ratio
2.0
3.5
3.6
4.7
1.7
2.3
3.1
4.8
7.6
17.2
Calculate and interpret the value of the correlation coefficient between sale price and size.
Calculate and interpret the value of the correlation coefficient between sale price and land-tobuilding ratio.
If you want to predict sale price and you could use either size or land-to-building ratio as the
basis for making predictions, which would you use? Explain.
Based on your choice in Part ©, find the equation of the least-squares regression line you would
use for predicting y = sale price.