the following questions: presented below to answer the following questions: Cyli

Question

the following questions: presented below to answer the following questions: Cylinder Strength at End of Various Duration of Curing Time Curing Time, days Compressive Strength, psi 700 4 1500 2500 12 3000 3500 3750 4000 24 4200 3a. What is the slope and intercept for a best fit linear line based on equation 5.d using the first and the last data point. 3b. Whatis the slope and intercept for a best fit linear line based on equations 6.28 and 6.29 3c. use the linear equation from problem 3a and the recorded raw strength in the above table to develop a table that is similar to table 6 3d. use the linear equation from problem 3b and recorded raw strength in the above table to the develop a table that is similar to table 6.7 3e. Compare and contrast the tables developed in problem 3c and in problem 3d

Explanation / Answer

3A. Best fit line by using equatin 6.5 using the first and last data point.

slope = (4200 -700)/(28-2) = 134.6153; c = 700- 134.62 * 2 = 430.77

equation is y = 134.62x + 430.77

where y = compressive strength in psi and x = curing time in days

i will do question 3(c) first here, which is to draw a table which is given here like in Table 6.7

Here the given table is presented above.

Now i will solve question 3.b By given two equations

Here y = 0 + 1 X

where y = compressive strength in psi and x = curing time in days

this is a linear regression equation

where  0 will be calculated by the equation 6.28

and 1 = [408000 - (23150*114)/8)]/ [ 2244- 1142/ 8] = 78112.5/619.5 = 126.09

Here the values for calculating the values for equation 6.29 is calculated from given table

0 = 2893.75 - 126.09* 14.25 = 1097

so y = 126.09x + 1097; where y = compressive strength in psi and x = curing time in days

(D) Table given below as desired

(e) In table in 3(b) the error is all positive and in 3(d), the error is negative positves both and average of all of them is 0, so it is a better regression model than the previous one.

Curing time Compressive strength Predicted Compressive strength Error 2 700 700.00 0.00 4 1500 969.23 530.77 8 2500 1507.69 992.31 12 3000 2046.15 953.85 16 3500 2584.61 915.39 20 3750 3123.08 626.92 24 4000 3661.54 338.46 28 4200 4200.00 0.00

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