Đáp án:
$A.\ Y_{tb} = 242,5268$
Giải thích các bước giải:
\(\begin{array}{l}
\begin{array}{|c|c|c|}\hline
X&Y&XY&X^2\\
\hline
2&258&516&4\\
\hline
2,25&245&551,25&5,0625\\
\hline
2,5&240&600&6,25\\
\hline
2,6&234&608,4&6,76\\
\hline
2,8&230&644&7,84\\
\hline
3&223&669&9\\
\hline
\end{array}\qquad \left.\begin{array}{l}\displaystyle\sum_{i=1}^6 X_i = 15,15\\\displaystyle\sum_{i=1}^6 Y_i = 1430\\
\displaystyle\sum_{i=1}^6 X_iY_i = 3588,65\\
\displaystyle\sum_{i=1}^5X_i^2 = 38,9125\end{array}\right.\\
\text{Ta có:}\\
\overline{X} = \dfrac16 \displaystyle\sum_{i=1}^6 X_i=\dfrac{15,15}{6} = 2,525\\
\overline{Y} = \dfrac16\displaystyle\sum_{i=1}^6 Y_i = \dfrac{1430}{6} = 238,333\\
\beta = \dfrac{\displaystyle\sum_{i=1}^6 X_iY_i - 6.\overline{X}\overline{Y}}{\displaystyle\sum_{i=1}^6 X_i^2 - 6.\displaystyle\sum_{i=1}^6 \overline{X}}= \dfrac{3588,65 - 6.2,525.238,333}{38,9125 - 6.2.525^2}= -33,5407211\\
\alpha = \overline{Y} - \beta\overline{X} = 238,333 + 33,5407211.2,525 = 323,023321\\
\text{Ta được:}\\
\quad Y =323,023321 - 33,5407211X\\
\text{Với}\ X = 2,4\ (1000\ USD),\ \text{ta được:}\\
\quad Y = 323,023321 - 33,5407211.2,4 = 242,5
\end{array}\)
