Dean Parmalee wished to know if the year-end grades assigned to Wright State University Medical School students are predictive of their second-year medical board scores.The following table shows, for 89 students, the year-end score (AVG, in percent of 100) and the score on the second year medical board (BOARD) examination (data:medscores.mtw).

a)Use the regression model to give 95% mean and individual prediction intervals for AVG score of 95.73 and 94.03. Make a graph showing the 95% confidence bands for the mean and the 95% prediction intervals.

AVG BOARD AVG BOARD AVG BOARD 95.73 257 85.91 208 82.01 196 94.03 256 85.81 210 81.86 179 91.51 242 185.35 212 81.7 207 91.49 223 185.3 225 81.65 202 91.13 241 185.27 203 81.51 230 90.88 234 85.05 214 81.07 200 90.83 226 84.58 176 80.95 200 90.6 236 84.51 196 80.92 160 90.3 250 84.51 207 80.84 205 90.29 226 84.42 207 80.77 194 89.93 233 84.34 211 80.72 196 89.83 241 84.34 202 80.69 171 89.65 234 84.13 229 80.58 201 89.47 231 84.13 202 80.57 177 88.87 228 84.09 184 80.1 192 88.8 229 83.98 206 79.38 187 88.66 235 83.93 202 78.75 161 88.55 216 83.92 176 78.32 172 88.43 207 83.73 204 78.17 163 88.34 224 83.47 208 77.39 166 87.95 237 83.27 211 76.3 170 87.79 213 83.13 196 75.85 159 87.01 215 83.05 203 75.6 154 86.86 187 83.02 188 75.16 169 86.85 204 82.82 169 74.85 159 86.84 219 182.78 205 74.66 167 86.3 228 182.57 183 74.58 154 86.13 210 82.56 181 74.16 148 86.1 216 82.45 173 70.34 159 85.92 212 82.24 185