### Predicting Porosity and Calculating Residuals#### (c) Predict Porosity When Unit Weight is 135- **Predicted Value**: \(\hat{y} = -3.401\) ✔ **Explanation**: When attempting to predict porosity for a unit weight of 135, it's important to note that this value is outside the scope of available data, leading to a prediction of a negative porosity value, which logically cannot occur. **Rationale**: Predicting beyond the data range (135 in this case) can lead to results that do not make sense in real-world applications.#### (d) Calculate Residuals1. **Residual for the First Observation** - **Calculated Residual**: \(-0.50\) ✖2. **Residual for the Second Observation** - **Calculated Value**: [Blank]**Note**: Residuals should be computed by finding the difference between the observed and predicted values, rounded to two decimal places.#### (e) Calculate a Point Estimate of \(\sigma\)- **Calculated Value**: [Blank]**Instructions**: Provide your answer rounded to two decimal places. The calculation of \(\sigma\) involves statistical estimation methods based on residual calculations.This guide highlights the challenges of extrapolation in statistical predictions and emphasizes accuracy in calculation methods, particularly with residuals and standard deviations. **No-Fines Concrete and Its Properties**No-fines concrete, composed of uniformly graded coarse aggregate and cement-water paste, is particularly effective in areas prone to excessive rainfall due to its excellent drainage properties. An article titled "Pavement Thickness Design for No-Fines Concrete Parking Lots" discusses the advantages and applications of this type of concrete.A least squares analysis was conducted to understand the relationship between porosity (y, in percentage) and unit weight (x, in pounds per cubic foot, pcf) in concrete specimens. Below is the representative data collected from the study:- **Figure 1: Data Table** - **First Dataset:** - x (Unit Weight in pcf): 99.2, 101.0, 102.6, 102.9, 105.5, 107.1, 108.9, 110.7 - y (Porosity in %): 28.9, 27.7, 26.8, 25.3, 22.9, 21.4, 21.0, 19.5 - **Second Dataset:** - x (Unit Weight in pcf): 112.0, 112.2, 113.5, 113.7, 115.3, 115.3, 120.1 - y (Porosity in %): 17.2, 18.8, 15.8, 16.9, 12.9, 13.7, 10.6The data reveals a negative correlation between unit weight and porosity, implying that as the unit weight increases, the porosity tends to decrease. This relationship is crucial for understanding and optimizing the performance of no-fines concrete in construction applications.

Given: x y 99.2 28.9 101 27.7 102.6 26.8 102.9 25.3 105.5 22.9 107.1 21.4 108.9…

Answered: (c) Predict porosity when unit weight…

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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A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were: y=ax+b a= -0.889 b=32.071 r2=0.505521 r= -0.711 Use this to predict the number of situps a person who watches 5 hours of TV can do (to one decimal place)
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You estimated a regression with the following output. Source | SS df MS Number of obs = 423 -------------+---------------------------------- F(1, 421) = 267.80 Model | 8758968.84 1 8758968.84 Prob > F = 0.0000 Residual | 13769523.8 421 32706.7074 R-squared = 0.3888 -------------+---------------------------------- Adj R-squared = 0.3873 Total | 22528492.7 422 53385.0537 Root MSE = 180.85 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 6.150402 .3758334 16.36 0.000 5.411658 6.889145 _cons | -8.022201 24.02003 -0.33 0.739 -55.23632 39.19192…
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y = 26.699 -0.639*x R² = 0.5 r = -0.704 Predict the number of situps a person who watches 6 hours of TV can do (round your answer to three decimal places).
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were y=ax+b a=-1.324 b=23.586 r2=0.887364 r=-0.942 Use this to predict the number of situps a person who watches 11.5 hours of TV can do (to one decimal place)
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were:y=ax+b a=-0.667 b=26.552 r2=0.677329 r=-0.823 Use this to predict the number of situps a person who watches 12 hours of TV can do (to one decimal place)

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