l0-fines concrete, made from a uniformly graded coarse aggregate and a cement-water paste. is beneficial in areas prone to excessive rainfall because of its excelient drainage properties. The article "Pavement Thickness Design for No-Fines Concrete Parking Lots." employed a least squares analysis in studying how yporosity () is related to unit weight (pef) in concrete specimens. Consider the following representative data * 99.2 101.O 102.6 102.9 105.5 107.1 108.9 110.7 y 20.9 27.7 26.8 25.3 22.9 21.4 21.0 19.5 * 112.0 112.2 113.5 113.7 115.3 115.3 120.1 Y 17.2 18. 15.0 16.9 12.9 13.7 10.6 A USE SALT alevant summary quantities are E, - 1640.0 r • 299.4, x² ▪ 179.826.14, x», ▪ 32.261.70. r - 6415.44, (a) Obtain the equation of the estimated regression line. (Round all numerical values to four decimal places.) Create a scatterplot of the data and graph the estimated line. y 125 30 125 120 120 25 25 115 115 20 20 110 110 15 105 15 105 100 100 10 10 10 15 20 25 105 115 15 25 30 100 105 115 120 125 100 110 120 10 110 Does it appear that the model relationship will explain a great deal of the observed variation in y? EeectV. the linear model explains a great deal of the variation in y since the accompanying fitted line plot eect-v show a very streng. linear association betveen unit weight and porosity . (b) Interpret the slope of the least squares line. (Round your ansver to four decimal places.) The slepe tells us that a one-pcf increase in the unit weight of a concrete specimen is associated with a percentage point decrease in the specimen's predicted porosity. (c) Predict poresity when unit weight is 1357 (Round your ansver to two decimal places.) Why is it not a good idea to predict porosity when unit weight is 1357 When we predict porosity for a unit weight of 135 (which is outside the scope of the data) the result i Select v which -Selectv happen in reality. (d) Calculate the residual corresponding to the first observation. (Round your ansver to tvo decimal places.) Calculate the residual corresponding to the second observation. (Round your ansvver to two decimal places.)
l0-fines concrete, made from a uniformly graded coarse aggregate and a cement-water paste. is beneficial in areas prone to excessive rainfall because of its excelient drainage properties. The article "Pavement Thickness Design for No-Fines Concrete Parking Lots." employed a least squares analysis in studying how yporosity () is related to unit weight (pef) in concrete specimens. Consider the following representative data * 99.2 101.O 102.6 102.9 105.5 107.1 108.9 110.7 y 20.9 27.7 26.8 25.3 22.9 21.4 21.0 19.5 * 112.0 112.2 113.5 113.7 115.3 115.3 120.1 Y 17.2 18. 15.0 16.9 12.9 13.7 10.6 A USE SALT alevant summary quantities are E, - 1640.0 r • 299.4, x² ▪ 179.826.14, x», ▪ 32.261.70. r - 6415.44, (a) Obtain the equation of the estimated regression line. (Round all numerical values to four decimal places.) Create a scatterplot of the data and graph the estimated line. y 125 30 125 120 120 25 25 115 115 20 20 110 110 15 105 15 105 100 100 10 10 10 15 20 25 105 115 15 25 30 100 105 115 120 125 100 110 120 10 110 Does it appear that the model relationship will explain a great deal of the observed variation in y? EeectV. the linear model explains a great deal of the variation in y since the accompanying fitted line plot eect-v show a very streng. linear association betveen unit weight and porosity . (b) Interpret the slope of the least squares line. (Round your ansver to four decimal places.) The slepe tells us that a one-pcf increase in the unit weight of a concrete specimen is associated with a percentage point decrease in the specimen's predicted porosity. (c) Predict poresity when unit weight is 1357 (Round your ansver to two decimal places.) Why is it not a good idea to predict porosity when unit weight is 1357 When we predict porosity for a unit weight of 135 (which is outside the scope of the data) the result i Select v which -Selectv happen in reality. (d) Calculate the residual corresponding to the first observation. (Round your ansver to tvo decimal places.) Calculate the residual corresponding to the second observation. (Round your ansvver to two decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:No-fines concrete, made from a uniformly graded coarse aggregate and a cement-water paste, is beneficial in areas prone to excessive rainfall because of its excellent drainage properties. The article "Pavement Thickness Design for No-Fines Concrete Parking Lots,"t employed a least squares analysis in studying how y = porosity (%) is related to
x = unit weight (pcf) in concrete specimens. Consider the following representative data.
x 99.2 101.0 102.6 102.9 105.5 107.1 108.9 110.7
y 28.9 27.7
26.8
25.3
22.9
21.4
21.0
19.5
x 112.0 112.2
113.5 113.7 115.3 115.3 120.1
y 17.2
18.8
15.8
16.9
12.9
13.7
10.6
In USE SALT
Relevant summary quantities are 5x, = 1640.0 YY, = 299.4, x = 179,826.14, xy, = 32,261.70, y? = 6415.44.
(a) Obtain the equation of the estimated regression line. (Round all numerical values to four decimal places.)
y =
Create a scatterplot of the data and graph the estimated line.
y
y
y
30
30
125
125
120
120
25
25
115
115
20
20
110
110
15
15
105
105
100
100
10
10
10
15
20
25
30
100
105
110
115
120
25
10
15
20
25
30
100
105
110
115
120
125
Does it appear that the model relationship will explain a great deal of the observed variation in y?
---Select--- v, the linear model explains a great deal of the variation in y since the accompanying fitted line plot ---Select--- v show a very strong, linear association between unit weight and porosity.
(b) Interpret the slope of the least squares line. (Round your answer to four decimal places.)
The slope tells us that a one-pcf increase in the unit weight of a concrete specimen is associated with a
percentage point decrease in the specimen's predicted porosity.
(c) Predict porosity when unit weight is 135? (Round your answer to two decimal places.)
Why is it not a good idea to predict porosity when unit weight is 135?
When we predict porosity for a unit weight of 135 (which is outside the scope of the data) the result is -Select- *
which ---Select-- V happen in reality.
(d) Calculate the residual corresponding to the first observation. (Round your answer to two decimal places.)
Calculate the residual corresponding to the second observation. (Round your answer to two decimal places.)
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