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 vwhich varying levels lateral pressure vwere 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 (E in MPa), the applied lateral pressure was equivalent to a fixed proportion of the specimen's f (0, 0.1f.. 0.6f ). Also, since bond strength can be heavily influenced by the specimen's f bond capacity was expressed as the ratio of bond strength (MPa) to v Pressure 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 Ratio 0.123 0.100 0.101 0.172 0.133 0.107 0.217 0.172 0.151 0.263 0.227 0.252 0.310 Pressure 0.4 .4 0.4 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 supports 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, 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 reasonably strong. positive, linear relationship betwveen pressure and the bond capacity ratio and supports the use of a simple linear regression model. O A scatterplot of the data shows a weak, positive, linear relationship bebween pressure and the bond capacity ratio and does not support the use of a simple linear regression model. (b) Use the accompanying Minitab output to give point estimates of the slope and intercept of the population regression line. (Enter your ansvers to five decimal places.) The regression equation is Ratio - 0.101 + 0.461 Pressure SE Coef 0.01308 Predictor Coef 0.000 0.000 Constant 0.10121 7.74 0.46071 R-Sg - 89.5% Pressure 0.03627 12.70 S = 0.0332397 R-Sq (adj) = 88.94 Analysis of Variance Source DF MS P Regression 1 0.17830 0.17830 161.37 0.000 Residual Error 19 0.02099 0.00110 Total 20 0.19929 slope intercept (c) Calculate a point estimate of the true average bond capacity when lateral pressure is 0.35f (Round your answer to four decimal places.)
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 vwhich varying levels lateral pressure vwere 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 (E in MPa), the applied lateral pressure was equivalent to a fixed proportion of the specimen's f (0, 0.1f.. 0.6f ). Also, since bond strength can be heavily influenced by the specimen's f bond capacity was expressed as the ratio of bond strength (MPa) to v Pressure 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.4 Ratio 0.123 0.100 0.101 0.172 0.133 0.107 0.217 0.172 0.151 0.263 0.227 0.252 0.310 Pressure 0.4 .4 0.4 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 supports 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, 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 reasonably strong. positive, linear relationship betwveen pressure and the bond capacity ratio and supports the use of a simple linear regression model. O A scatterplot of the data shows a weak, positive, linear relationship bebween pressure and the bond capacity ratio and does not support the use of a simple linear regression model. (b) Use the accompanying Minitab output to give point estimates of the slope and intercept of the population regression line. (Enter your ansvers to five decimal places.) The regression equation is Ratio - 0.101 + 0.461 Pressure SE Coef 0.01308 Predictor Coef 0.000 0.000 Constant 0.10121 7.74 0.46071 R-Sg - 89.5% Pressure 0.03627 12.70 S = 0.0332397 R-Sq (adj) = 88.94 Analysis of Variance Source DF MS P Regression 1 0.17830 0.17830 161.37 0.000 Residual Error 19 0.02099 0.00110 Total 20 0.19929 slope intercept (c) Calculate a point estimate of the true average bond capacity when lateral pressure is 0.35f (Round your answer to four decimal places.)
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Transcribed Image Text:(d) What is a point estimate of the error standard deviation o? (Enter your ansvwer to seven decimal places.)
How would you interpret the point estimate of the error standard deviation o?
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.
O This represents the typical difference between the lateral pressure applied to a bar and the ratio predicted by the least squares regression line.
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 a concrete specimen's actual bond capacity ratio and the lateral pressure predicted by the least squares regression line.
This represents the ratio predicted by the least squares regression line for a value of 1.
(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.)
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 (f, in MPa), the applied lateral pressure was equivalent to a fixed
proportion of the specimen's f (0, 0.1f.., 0.6f). Also, since bond strength can be heavily influenced by the specimen's f bond capacity was expressed as the ratio of bond strength (MPa) to vf.
cu'
cu
Pressure
0.1
0.1
0.1
0.2
0.2
0.2
0.3
0.3
0.3
0.4
Ratio
0.123 0.100 0.101 0.172
0.133 0.107 0.217 0.172 0.151 0.263 0.227 0.252 0.310
Pressure
0.4
0.4
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 supports 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, 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 reasonably strong, positive, 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 weak, positive, linear relationship between pressure and the bond capacity ratio and does not support the use of a simple linear regression model.
(b) 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
Predictor
Сoef
T
P
Constant
0.10121
0.01308
7.74
0.000
Pressure
0.46071
0.03627
12.70
0.000
S = 0.0332397
R-Sq = 89.5%
R-Sq (adj) = 88.9%
Analysis of Variance
Source
DF
MS
F
P
Regression
1
0.17830
0.17830
161.37
0.000
Residual Error
19
0.02099
0.00110
Total
20
0.19929
slope
intercept
(c) Calculate a point estimate of the true average bond capacity when lateral pressure is 0.35f (Round your answer to four decimal places.)
cu
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