The bond behavior of reinforcing bars is an important determinant of strength and stability. The article "Experimental Study on the Bond Behavior of Reinforcing Bars Embedded in Concrete Subjected to Lateral Pressure"t reported the results of one experiment in which varying levels of lateral pressure were applied to 21 concrete cube specimens, each with an embedded 16 mm plain steel round bar, and the corresponding bond capacity was determined. Due to differing concrete cube strengths in MPa), the applied lateral pressure was equivalent to a fixed proportion of the specimen's e, a e Also, since bond strength can be heavily influenced by the specimen's bond capacity was expressed as the ratio of bond strength (MPa) to Pressure • a1 a a 02 a2 2 3 03 03 04 Ratie e.123 0.100 e.1es G1n a133 0.1er e217 e172 e151 0263 0227 e 252 e310 Pressure 04 34 05 05 0.s 04 04 04 0.3es 029 es 0319 0312 0394 3 0320 Ratie ( Does a scatterplot of the data support the use of the simple linear regression model? OA scatterplot of the data shows a reasonably strong, negative, linear relationship between pressure and the bond capacity ratio and does not support the use of a simple linear regression model. O A scatterplot of the data shows a weak, positive, linear relationship between pressure and the bond capacity ratio and does not support the use of a simple linear regression model. O A scatterplot of the data shows a weak, negative, linear relationship between pressure and the bond capacity ratio and supports the use of a simple linear regression model. O A scatterplot of the data shows a reasonably strong, positive, linear relationship between pressure and the bond capacity ratio and supports the use of a simple linear regression model. OA scatterplot of the data shows a reasonably strong, negative, linear relationship between pressure and the bond capacity ratio and supports the use of a simple linear regression model. Use the accompanying Minitab output to give point estimates of the slope and intercept of the population regression line. (Enter your answers to five decimal places.) regression equation is Ratio - 0.101 + 0.461 Pressure SE Ceet The Predietor Coef Censtant 0.1 0.0130 7.74 0.c00 Pressure 0.03627 12.70 0.000 S- 0.0332397 R-Sg - 89.51 R-3qladj) - 88.9 Analysis of Variance Seurce DF egression 0.17830 0.130 161.37 0.000 Residual Ezor 19 0.0209 0.00110 Tetal 20 0.19929 epe wtercept a Calculate a point estimate of the true average bond capacity when lateral pressure is cou (Round your answer to four decimal places.) o What is a point estimate of the error standard deviation a? (Enter your answer to seven decimal places.) How would you interpret the point estimate of the error standard deviation a? O This represents the typical difference between a concrete specimen's actual bond capacity ratio and the lateral pressure predicted by the least squares regression line. O This represents the ratio predicted by the least squares regression line for a value of 1. O This represents the typical difference between a concrete specimen's actual bond capacity ratio and the ratio predicted by the least squares regression line. This represents the typical difference between the lateral pressure applied to a bar and the ratio predicted by the least squares regression line. O This represents the typical difference between the lateral pressure applied to a bar and the lateral pressure predicted by the least squares regression line. What is the value of total variation? (Enter your answer to five decimal places.) e What percentage of it can be explained by the model relationship? (Enter your answer to one decimal place.) x %

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The bond behavior of reinforcing bars is an important determinant of
strength and stability. The article "Experimental Study on the Bond Behavior
of Reinforcing Bars Embedded in Concrete Subjected to Lateral Pressure"t
reported the results of one experiment in which varying levels of lateral
pressure were applied to 21 concrete cube specimens, each with an
embedded 16 mm plain steel round bar, and the corresponding bond
capacity was determined. Due to differing concrete cube strengths in
MPa), the applied lateral pressure was equivalent to a fixed proportion of the
specimen's (0, a.1a. Also, since bond strength can be heavily
influenced by the specimen's bond capacity was expressed as the ratio of
bond strength (MPa) to v
Pressure o
0 0 0 0.1
0.123 0.100 0.101 0.172 0.133 0.107 0.217 0.172 0.151 0.263 0.227 0.2s2 0.310
0.1 0.1
0.2
0.2
0.2
0.3 0.3 03 0.4
Ratio
Pressure 04 04
0.5 0.5
0.5 0.6
0.6
0.6
Ratio
0.365 0.239 0.365 0.319 0.312 0.394 0.386 0.320
(a) Does a scatterplot of the data support the use of the simple linear
regression model?
O A scatterplot of the data shows a reasonably strong, negative, linear
relationship between pressure and the bond capacity ratio and does
not support the use of a simple linear regression model.
OA scatterplot of the data shows a weak, positive, linear relationship
between pressure and the bond capacity ratio and does not support
the use of a simple linear regression model.
OA scatterplot of the data shows a weak, negative, linear relationship
between pressure and the bond capacity ratio and supports the use
of a simple linear regression model.
OA scatterplot of the data shows a reasonably strong, positive, linear
relationship between pressure and the bond capacity ratio and
supports the use of a simple linear regression model.
OA scatterplot of the data shows a reasonably strong, negative, linear
relationship between pressure and the bond capacity ratio and
supports the use of a simple linear regression model.
() Use the accompanying Minitab output to give point estimates of the slope
and intercept of the population regression line. (Enter your answers to
five decimal places.)
The regression equation is Ratio - 0.101 + 0.461 Pressure
SE Coef
0.0130
Predietor
Coef
Constant
0.10121
7.74
0.000
Pressure
0.46071
0.03627
12.70
0.000
S- 0.0332397
R-Sq - 89.5%
R-Sq (adj) - 88.94
Analysis of Variance
Source
DF
MS
Regression
1
0.17830
0.17830
161.37
0.000
Residual ErrOr
19
0.02099
0.00110
Total
20
0.19929
slope
04071
intercept
0. 10121
(
o Calculate a point estimate of the true average bond capacity when lateral
pressure is 0.0 (Round your answer to four decimal places.)
0.116
(4) What is a point estimate of the error standard deviation a? (Enter your
answer to seven decimal places.)
00332307
How would you interpret the point estimate of the error standard
deviation a?
o This represents the typical difference between a concrete
specimen's actual bond capacity ratio and the lateral pressure
predicted by the least squares regression line.
O This represents the ratio predicted by the least squares regression
line for a value of 1.
O This represents the typical difference between a concrete
specimen's actual bond capacity ratio and the ratio predicted by the
least squares regression line.
O This represents the typical difference between the lateral pressure
applied to a bar and the ratio predicted by the least squares
regression line.
O This represents the typical difference between the lateral pressure
applied to a bar and the lateral pressure predicted by the least
squares regression line.
(e) What is the value of total variation? (Enter your answer to five decimal
places.)
What percentage of it can be explained by the model relationship? (Enter
your answer to one decimal place.)
89.5%
Transcribed Image Text:The bond behavior of reinforcing bars is an important determinant of strength and stability. The article "Experimental Study on the Bond Behavior of Reinforcing Bars Embedded in Concrete Subjected to Lateral Pressure"t reported the results of one experiment in which varying levels of lateral pressure were applied to 21 concrete cube specimens, each with an embedded 16 mm plain steel round bar, and the corresponding bond capacity was determined. Due to differing concrete cube strengths in MPa), the applied lateral pressure was equivalent to a fixed proportion of the specimen's (0, a.1a. Also, since bond strength can be heavily influenced by the specimen's bond capacity was expressed as the ratio of bond strength (MPa) to v Pressure o 0 0 0 0.1 0.123 0.100 0.101 0.172 0.133 0.107 0.217 0.172 0.151 0.263 0.227 0.2s2 0.310 0.1 0.1 0.2 0.2 0.2 0.3 0.3 03 0.4 Ratio Pressure 04 04 0.5 0.5 0.5 0.6 0.6 0.6 Ratio 0.365 0.239 0.365 0.319 0.312 0.394 0.386 0.320 (a) Does a scatterplot of the data support the use of the simple linear regression model? O A scatterplot of the data shows a reasonably strong, negative, linear relationship between pressure and the bond capacity ratio and does not support the use of a simple linear regression model. OA scatterplot of the data shows a weak, positive, linear relationship between pressure and the bond capacity ratio and does not support the use of a simple linear regression model. OA scatterplot of the data shows a weak, negative, linear relationship between pressure and the bond capacity ratio and supports the use of a simple linear regression model. OA scatterplot of the data shows a reasonably strong, positive, linear relationship between pressure and the bond capacity ratio and supports the use of a simple linear regression model. OA scatterplot of the data shows a reasonably strong, negative, linear relationship between pressure and the bond capacity ratio and supports the use of a simple linear regression model. () Use the accompanying Minitab output to give point estimates of the slope and intercept of the population regression line. (Enter your answers to five decimal places.) The regression equation is Ratio - 0.101 + 0.461 Pressure SE Coef 0.0130 Predietor Coef Constant 0.10121 7.74 0.000 Pressure 0.46071 0.03627 12.70 0.000 S- 0.0332397 R-Sq - 89.5% R-Sq (adj) - 88.94 Analysis of Variance Source DF MS Regression 1 0.17830 0.17830 161.37 0.000 Residual ErrOr 19 0.02099 0.00110 Total 20 0.19929 slope 04071 intercept 0. 10121 ( o Calculate a point estimate of the true average bond capacity when lateral pressure is 0.0 (Round your answer to four decimal places.) 0.116 (4) What is a point estimate of the error standard deviation a? (Enter your answer to seven decimal places.) 00332307 How would you interpret the point estimate of the error standard deviation a? o This represents the typical difference between a concrete specimen's actual bond capacity ratio and the lateral pressure predicted by the least squares regression line. O This represents the ratio predicted by the least squares regression line for a value of 1. O This represents the typical difference between a concrete specimen's actual bond capacity ratio and the ratio predicted by the least squares regression line. O This represents the typical difference between the lateral pressure applied to a bar and the ratio predicted by the least squares regression line. O This represents the typical difference between the lateral pressure applied to a bar and the lateral pressure predicted by the least squares regression line. (e) What is the value of total variation? (Enter your answer to five decimal places.) What percentage of it can be explained by the model relationship? (Enter your answer to one decimal place.) 89.5%
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