The data in this question consist of measurements on n = 21 100-year old marble tombstones in various cities across the USA. It is believed that air pollution affects the deterioration of marble tombstones by steadily eroding the surface, causing the tombstone size to slowly decrease as well as affecting the aesthetic nish of the stone. In a study by TC. Meierding (1993), air pollution is characterized by the average concentration of sulfur dioxide (802) over a IOU-year period, and the deterioration of marble tombstones was measured as the decrease in thickness of the tombstone where it is exposed to the atmOSphere relative to where it is unexposed. The following variables were recorded for this study: 0 SD22 mean lOO-year 502 concentration in each city, measured in pg/m3; o Irate: mean surface recession rate, measured in mm / 100years. A simple linear regression model that used 802 to predict Irate was t using the data. A plot of the data with the estimated regression line is shown below, along with some summary statistics about the variables and standard regression model output. (Note you will not have access to the raw data for this question, just the summaries provided below). sample mean sample variance S02 136.5238 7382.362 rrate 1.49619 0.6717248 Table 1: Summary statistics for tombstone data. Call : 1m (formula = rrate ~ $02, data = dat) Coefficients : Estimate Std. Error t value Pr (> |t|) (Intercept) 0.3229959 0. 1521958 2. 122 0. 0472 * S02 0 . 0085933 0. 0009499 9. 046 2. 58e-08 *** Signif. codes: 0 '***' 0.001 '** ' 0.01 '*' 0.05 '. ' 0.1 ' ) 1 Residual standard error: 0.365 on 19 degrees of freedom Multiple R-squared: 0. 8116, Adjusted R-squared: 0.8017(b) (2 pts) Use the fitted model to predict a future, unobserved mean surface recession rate for a specific tombstone exposed to an a mean 100-year SO2 concentration of 100 ug/m3. Show your work mathematically (no code required).(c) (3 pts) Compute the standard error of your prediction from part (b). You may use the fact that the sum of squares for the mean 100-year SO2 concentrations is 147647.2. Show your work mathematically (no code required)