A transportation engineer had an idea to develop a nondestructive test for determining the percentage of air void in asphalt pavement by sensing the dielectric properties of the pavement. To determine if there is a relationship between the two, the engineer collected a random sample of 18 small asphalt sections and measured both the dielectric constant and air void percentage. The data is found in the table. Run a simple linear regression (least squares) model with R using dielectric constant and the predictor and air void % as the response and answer the following questions.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

dielectric_const 4.55 4.49 4.50 4.47 4.47 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.33 4.44 4.40 4.26 4.32 4.34

air_void 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.08

1. Using diagnostic plots, assess whether or not the assumptions of normally distributed, zero-meaned errors with constant variance are reasonable.
2. Is there a statistically significant relationship between dielectric constant and air void %? How much of the variability in air void % can be explained by dielectric constant?
3. State the estimates for intercept and slope. Is there sufficient evidence to conclude they are both different from zero? Compute 95% confidence intervals for both estimates.
4. Create a grid of potential dielectric constant values ranging from 4.20 to 4.60 with spacing of at most 0.01 and predict values of air void % in your grid; also calculate values for the 95% confidence interval and the 95% prediction interval. Plot the predicted values versus your grid of dielectric constant values. Overlay the confidence and prediction limits using dashed and dotted lines, respectively; also overlay the actual air void % values as points. Does the 95% prediction interval seem reasonable?