Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit

Question

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: Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in the data above resulted in y = 7.584 s_Y = 0.180 when x = 40 and y = 9.716, s_y = 0.255 for x = 60

Explanation / Answer

Predicted value of y when x=40 is 7.584 and predicted value of y when x=60 is 9.716

Now, we would calculate the average of 7.584 and 9.716 which is 8.65.

Now, calculate the difference i.e.7.584-8.65=-1.066 and 9.716-8.65=1.066 and square and add them. Therefore, (-1.066)^2+(1.066)^2=1.136356+1.136356=2.272712.

Hence, 2.272712 is the correct answer

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