A study was conducted to determine the association between the maximum distance at which a highway sign can be read (in feet) and the driver's age (in years). Thirty drivers of various ages were studied. Sample means and variances for distance and age, and the correlation between these two variables, are given in the table below. Sample Mean Sample Variance Distance (Y) 423.33 6678.5 Age (X) 51 474.21 = 0.81 = 30 We want to estimate the following regression equation. = 0 + 1 Use the above information and answer the following questions. Note that 2 = 2 and = ( ) = ( 1) 2 . a) Find 0 and 1 and provide the estimated (fitted) regression equation. Interpret the slope. b) Find the standard error of 0 and 1 . Hint: First, obtain from 2 and then . c) Is "Age" a significant predictor of "Distance" in this linear model? Conduct a formal hypothesis test at a 5% significance level (include all the steps of the hypothesis testing). d) Construct a 95% confidence interval for the slope of this regression line. e) Considering the lower and upper 95% confidence limits of the slope calculated in part