A new material’s rupture strength (Y) is tested and compared against its compressive strength (X).  The desire is to need only test for the compressive strength and be able to infer other properties.  The data is available in the accompanying spreadsheet.

TASKS (30, 30, and 10 points, respectively)

1. Assuming that a simple linear regression model is appropriate, fit a least squares regression model relating rupture (Y) to compression (X) and conduct appropriate tests. For example:

Test the hypothesis for the slope being equal to zero, i.e., that H_o: b₁ = 0, and H₁: b₁ ≠ 0 using a = 0.05.  Find the P-value for this test. Create and interpret appropriate plots of the residuals: residuals versus the predicted y, residuals versus the independent x, and a normal probability of the standardized residual.  In your interpretation, be sure to discuss what it is that you are looking for and why that matters.

1. Historically, this type of material has used a model for this situation that is a function of the square root of X. Transform the data (for every (X,Y) coordinate pair, create andplot (X⁵,Y)) and fit a least squares regression model.  Conduct appropriate analyses and interpretations of that model.
2. Discuss which model, from a statistical perspective, appears to be the most reasonable.