1. Read into R. Use response variable = Marble Tombstone Mean Surface Recession Rate, and covariate = Mean SO2 concentrations over a 100 year period. Description: Marble Tombstone Mean Surface Recession Rates and Mean SO2 concentrations over a 100 year period.

2. Obtain R2 , explain what it means.

3. Perform the following hypothesis testing and interval estimation using lm() and other related R functions.

3.1. Perform hypothesis tests for each coefficient, obtain p values, interpret the results, make a conclusion (i.e. reject or not reject) and explain why. Note: please explain what the null hypothesis is.

3.2. Compute interval estimation for coefficients, interpret the meanings of these quantities.

3.3. Make prediction of the Recession Rate at the 1^st, 2^nd, 3^rd, ., 99^th percentiles of the SO2, and obtain their prediction intervals (two types of the intervals).

3.4. Plot data points, the regression line, the predictions and its intervals (two types) and show that the interval is wider on both sides and narrow in the center.

3.5. Making prediction at what range of values of SO2 would be considered extrapolation? Is it OK to do extrapolation in this case?

4. Repeat the same questions (1-3) for the date set . Description: Cross-sectional analysis of 24 British bus companies (1951). Use response variable = Expenses per car mile (pence), covariate = Car miles per year (1000s).

tombstone

bus

1 City 2 Washington,DC (Rural) 3 Cincinnati,OH (Rural 4 Philadelphia,PA (Rura 5 Richmond,VA 6 Fall River,MA 7 Hartford,CT 8 Evanston,IL 9 Albany,NY 10 Washington, DC 11 Louisville,KY 12 Providence,RI 13 Cambridge,MA 14 Baltimore,MD 15 Newark,NJ 16 Boston,MA 17 Pittsburgh,PA 18 Cincinnati,OH 19 Brooklyn,NY 20 Philadelphia,PA 21 Indianapolis, IN 22 Chicago,IL Modelled Marble Tombstone Mean Surface Recession Rate (mm/100years) 12 20 20 46 48 92 91 94 102 0.27 0.14 0.33 0.81 0.84 1.08 1.78 1.21 1.09 1.72 1.18 1.01 122 142 142 178 180 197 224 234 239 244 323 1.98 1.53 2.71 2.41 1.61 2.51 2.15 3.16 1 24-23 8 4 2 ts 5. 03 7. .1 3 3 133 898 25-99 996 0 9 162 1 8 2 355 1e 50 9 0 1 2 1 112 41 5 2 81718677167166 11211 123456789 012345678901