Question

Asked Jul 29, 2019

Hi. I need help with part (d) and (e)

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"† 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_{cu}, in MPa), the applied lateral pressure was equivalent to a fixed proportion of the specimen's f_{cu }(0, 0.1f_{cu}, , 0.6f_{cu}).

Also, since bond strength can be heavily influenced by the specimen's
f_{cu}, bond capacity was expressed as the ratio of bond strength (MPa) to sqrt. of f_{cu}

.

Pressure | 0 | 0 | 0 | 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 |

(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 | ||||

Predictor | Coef | SE Coef | 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 | SS | 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

0.32f_{cu}.

(Round your answer to four decimal places.)(d)

What is a point estimate of the error standard deviation σ? (Enter your answer to seven decimal places.)

How would you interpret the point estimate of the error standard deviation σ?

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. 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 typical difference between the lateral pressure applied to a bar 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.)

%

Step 1

**(d) The error standard deviation:**

The formula to estimate the standard deviation (*σ*) of the error (*ε*) is as follows.

Step 2

**Point estimate of the error standard deviation σ:**

From the given MINITAB output in Part (b), the value of *s* is observed to be **0.0332397**.

**Interpretation:**

This represents the typical difference between a concrete specimen’s actual bond capacity ratio and the ratio predicted by the least squares regression line.

Step 3

**(e) Value of total variation:**

The SST is the measure of total variation in the response variable. It is sum of SSR and SSE

From the given MINITAB output in Part (b), the value of SST is **0.19929.**

**Coefficient of determination:**

The percentage of total variation (SST) explained by the regression&nb...

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