Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relationship with Density" (J. of Transp. Engr., 2011: 104-111), was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt content:

The following R output is from a simple linear regression of y on x:

a. Obtain the equation of the least squares line and interpret its slope.
b. What proportion of observed variation in dielectric constant can be attributed to the approximate linear relationship between dielectric constant and air void.
c. Does there appear to be a useful linear relationship between dielectric constant and air void? State and test the appropriate hypotheses.
d. Suppose it had previously been believed that when air void increased by 1 percent, the associated true average change in dielectric constant would be at least 2.05. Does the sample data contradict this belief? Carry out a test of appropriate hypotheses using a significance level of .01.

y 4.55 4.49 4.50 4.47 4.47 4.45 4.40 4.34 4.43 x 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 | 4.43 4.42 4.40 4.33 4.44 4.40 4.26 4.32 4.34 x5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.08 (Intercept) 4.858691 AirVoid Estimate Std. Error t value Pr(>t |) F) 1.214e- 06 Df Airvoid 1 0.071422 0.071422 56.635 Residuals 16 0.20178 0.001261