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Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data (read from a graph in the article "Effects of Aggregates and Microfillers on the Flexural Properties of Concrete"t). MOE 29.8 33.2 33.7 35.3 35.5 36.1 36.2 36.3 37.5 37.7 38.7 38.8 39.6 41.0 Strength 5.9 7.2 7.3 6.3 7.9 9.0 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 MOE 42.8 42.8 43.5 45.6 46.0 46.9 48.0 49.3 51.7 62.6 69.8 79.5 80.0 Strength 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7 (a) Construct a stem-and-leaf display of the MOE values. (Round each value down to the nearest whole number. Enter numbers from smallest to largest separated by spaces. Enter NONE for s with no values. Split the stems, placing leaves 0 to 4 on the first stem and leaves 5 to 9 on the second stem of the same value. Use the tens digit as the stem and the ones digit as the leat stem leaf 2

Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data (read from a graph in the article "Effects of Aggregates and Microfillers on the Flexural Properties of Concrete"t). MOE 29.8 33.2 33.7 35.3 35.5 36.1 36.2 36.3 37.5 37.7 38.7 38.8 39.6 41.0 Strength 5.9 7.2 7.3 6.3 7.9 9.0 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 MOE 42.8 42.8 43.5 45.6 46.0 46.9 48.0 49.3 51.7 62.6 69.8 79.5 80.0 Strength 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7 (a) Construct a stem-and-leaf display of the MOE values. (Round each value down to the nearest whole number. Enter numbers from smallest to largest separated by spaces. Enter NONE for s with no values. Split the stems, placing leaves 0 to 4 on the first stem and leaves 5 to 9 on the second stem of the same value. Use the tens digit as the stem and the ones digit as the leat stem leaf 2

MATLAB: An Introduction with Applications
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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Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data (read from a graph in the article "Effects of Aggregates and Microfillers on the Flexural Properties of Concrete"t). MOE 29.8 33.2 33.7 35.3 35.5 36.1 36.2 36.3 37.5 37.7 38.7 38.8 39.6 41.0 Strength 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 MOE 42.8 42.8 43.5 45.6 46.0 46.9 48.0 49.3 51.7 62.6 69.8 79.5 80.0 Strength 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7 (a) Construct a stem-and-leaf display of the MOE values. (Round each value down to the nearest whole number. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values. Split the stems, plading leaves 0 to 4 on the first stem and leaves 5 to 9 on the second stem of the same value. Use the tens digit as the stem and the ones digit as the leaf.) stem leaf 2 3 3 4 7 8. 8 Comment on any interesting features. (Select all that apply.) O There is a small amount of variation in the data. O There is some negative skew in the data. O There are some potential outliers. There is some positive skew in the data. There is a reasonably large amount of variation in the data. (b) Is the value of strength completely and uniquely determined by the value of MOE? Explain. O No, the strength values are completely and uniquely determined by MOE values. O Yes, multiple strength values are completely and uniquely determined by MOE values. O Yes, the strength values are not completely and uniquely determined by MOE values. No, the strength values are not completely and uniquely determined by MOE values. (c) Use the accompanying Minitab output to obtain the equation of the least squares line for predicting strength from modulus of elasticity. (Enter your slope to five decimal places, and your intercept to four decimal places.) Predictor Coef Stdev t-ratio P Constant 3.2925 0.6008 5.48 0.000 mod elas 0.10748 0.01280 8.40 0.000 S = 0.8657 R-sq = 73.8% R-sq (adj) = 72.88 Analysis of Variance SOURCE DF MS Regression 1 52.870 52.870 70.55 0.000 Error 25 18.736 0.749 Total 26 71.605 y = 2.
Transcribed Image Text:Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data (read from a graph in the article "Effects of Aggregates and Microfillers on the Flexural Properties of Concrete"t). MOE 29.8 33.2 33.7 35.3 35.5 36.1 36.2 36.3 37.5 37.7 38.7 38.8 39.6 41.0 Strength 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 MOE 42.8 42.8 43.5 45.6 46.0 46.9 48.0 49.3 51.7 62.6 69.8 79.5 80.0 Strength 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7 (a) Construct a stem-and-leaf display of the MOE values. (Round each value down to the nearest whole number. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values. Split the stems, plading leaves 0 to 4 on the first stem and leaves 5 to 9 on the second stem of the same value. Use the tens digit as the stem and the ones digit as the leaf.) stem leaf 2 3 3 4 7 8. 8 Comment on any interesting features. (Select all that apply.) O There is a small amount of variation in the data. O There is some negative skew in the data. O There are some potential outliers. There is some positive skew in the data. There is a reasonably large amount of variation in the data. (b) Is the value of strength completely and uniquely determined by the value of MOE? Explain. O No, the strength values are completely and uniquely determined by MOE values. O Yes, multiple strength values are completely and uniquely determined by MOE values. O Yes, the strength values are not completely and uniquely determined by MOE values. No, the strength values are not completely and uniquely determined by MOE values. (c) Use the accompanying Minitab output to obtain the equation of the least squares line for predicting strength from modulus of elasticity. (Enter your slope to five decimal places, and your intercept to four decimal places.) Predictor Coef Stdev t-ratio P Constant 3.2925 0.6008 5.48 0.000 mod elas 0.10748 0.01280 8.40 0.000 S = 0.8657 R-sq = 73.8% R-sq (adj) = 72.88 Analysis of Variance SOURCE DF MS Regression 1 52.870 52.870 70.55 0.000 Error 25 18.736 0.749 Total 26 71.605 y = 2.
Predict strength for a beam whose modulus of elasticity is 70. (Round your answer to two decimal places.) Would you feel comfortable using the least squares line to predict strength when modulus of elasticity is 1007 Explain. O No, this value is way beyond of the range the y values of the data values. Yes, this value is inside of the range the x values of the data values. Yes, this value is inside of the range the y values of the data values. No, this value is way beyond of the range the x values of the data values. (d) What are the values of SSE, SST, and the coefficient of determination? (Enter your answers to three decimal places.) SSE = SST = Do these values suggest that the simple linear regression model effectively describes the relationship between the two variables? Explain. The 2 value is large, which suggests that the linear relationship is not a useful approximation to the true relationship between these two variables. The r? value is large, which suggests that the linear relationship is a useful approximation to the true relationship between these two variables. The r2 value is small, which suggests that the linear relationship is a useful approximation to the true relationship between these two variables. The r value is small, which suggests that the linear relationship is not a useful approximation to the true relationship between these two variables.
Transcribed Image Text:Predict strength for a beam whose modulus of elasticity is 70. (Round your answer to two decimal places.) Would you feel comfortable using the least squares line to predict strength when modulus of elasticity is 1007 Explain. O No, this value is way beyond of the range the y values of the data values. Yes, this value is inside of the range the x values of the data values. Yes, this value is inside of the range the y values of the data values. No, this value is way beyond of the range the x values of the data values. (d) What are the values of SSE, SST, and the coefficient of determination? (Enter your answers to three decimal places.) SSE = SST = Do these values suggest that the simple linear regression model effectively describes the relationship between the two variables? Explain. The 2 value is large, which suggests that the linear relationship is not a useful approximation to the true relationship between these two variables. The r? value is large, which suggests that the linear relationship is a useful approximation to the true relationship between these two variables. The r2 value is small, which suggests that the linear relationship is a useful approximation to the true relationship between these two variables. The r value is small, which suggests that the linear relationship is not a useful approximation to the true relationship between these two variables.
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