5. An experiment was conducted regarding a quantitative analysis of factors found in high-density lipoprotein (HDL) in a sample of human blood serum. Three variables thought to be predictive of, or associated with, HDL measurement \( (Y) \) were the total cholesterol \( \left(X_{1}\right) \) and total triglyceride \( \left(X_{2}\right) \) concentrations in the sample, plus the presence or absence of a certain sticky component of the serum called sinking pre-beta or SPB \( \left(X_{3}\right) \), coded as 0 if absent and 1 if present. The data obtained are shown in the following table.
a. Test whether \( X_{1}, X_{2} \), or \( X_{3} \) alone significantly helps to predict \( Y \).
b. Test whether \( X_{1}, X_{2} \), and \( X_{3} \) taken together significantly help to predict \( Y \).
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline\( Y \) & \( X_{1} \) & \( X_{2} \) & \( X_{3} \) & \( Y \) & \( X_{1} \) & \( X_{2} \) & \( X_{3} \) & \( Y \) & \( X_{1} \) & \( X_{2} \) & \( X_{3} \) \\
\hline 47 & 287 & 111 & 0 & 63 & 339 & 168 & 1 & 36 & 318 & 180 & 0 \\
\hline 38 & 236 & 135 & 0 & 40 & 161 & 68 & 1 & 42 & 270 & 134 & 0 \\
\hline 47 & 255 & 98 & 0 & 59 & 324 & 92 & 1 & 41 & 262 & 154 & 0 \\
\hline 39 & 135 & 63 & 0 & 56 & 171 & 56 & 1 & 42 & 264 & 86 & 0 \\
\hline 44 & 121 & 46 & 0 & 76 & 265 & 240 & 1 & 39 & 325 & 148 & 0 \\
\hline 64 & 171 & 103 & 0 & 67 & 280 & 306 & 1 & 27 & 388 & 191 & 0 \\
\hline 58 & 260 & 227 & 0 & 57 & 248 & 93 & 1 & 31 & 260 & 123 & 0 \\
\hline 49 & 237 & 157 & 0 & 57 & 192 & 115 & 1 & 39 & 284 & 135 & 0 \\
\hline 55 & 261 & 266 & 0 & 42 & 349 & 408 & 1 & 56 & 326 & 236 & 1 \\
\hline 52 & 397 & 167 & 0 & 54 & 263 & 103 & 1 & 40 & 248 & 92 & 1 \\
\hline 49 & 295 & 164 & 0 & 60 & 223 & 102 & 1 & 58 & 285 & 153 & 1 \\
\hline 47 & 261 & 119 & 1 & 33 & 316 & 274 & 0 & 43 & 361 & 126 & 1 \\
\hline 40 & 258 & 145 & 1 & 55 & 288 & 130 & 0 & 40 & 248 & 226 & 1 \\
\hline 42 & 280 & 247 & 1 & 36 & 256 & 149 & 0 & 46 & 280 & 176 & 1 \\
\hline
\end{tabular}