Civil engineers often use the straight-line equation E(y) = o + 1 x to model

Civil engineers often use the straight-line equation E(y) = β_o + β₁x to model the relationship between the mean shear strength E(y) of masonry joints and pre compression stress x. To test this theory, a series of stress tests was performed on solid bricks arranged in triplets and joined with mortar (Proceedings of the Institute of Civil Engineers, Mar. 1990). The pre compression stress was varied for each triplet and the ultimate shear load just before failure (called the shear strength) was recorded. The stress results for 7 triplets (measured in N/mm²) are shown in the table below.

a. Plot the seven data points in a scatter gram. Does the relationship between shear strength and pre compression stress appear to be linear?

b. Use the method of least squares to estimate the parameters
of the linear model.

c. Interpret the values of β̂_o and β̂₁.

d. Conduct a test to determine if the slope, β̂₁, is positive      

 

Transcribed Image Text:

TRIPLETS Triplet Test 1 2 3 4 5 7 Shear Strength, y 1.00 2.18 2.24 2.41 2.59 2.82 3.06 Precompression Stress, x 0 .60 1.20 1.33 1.43 1.75 1.75