Consider the Table Below Which Displays the Price of a Commodity

Essay

Consider the table below which displays the price of a commodity for six consecutive years.
$\begin{array}{c|c}\hline \text { Year } & \text { Price (dollars) } \\\hline 1 & 250 \\\hline 2 & 255 \\\hline 3 & 253 \\\hline 4 & 255 \\\hline 5 & 259 \\\hline 6 & 261 \\\hline\end{array}$

a. Use the method of least squares to fit the model $E \left( Y _ { t } \right) = \beta _ { 0 } + \beta _ { 1 } t$ to the data. Write the prediction equation.
b. Use the prediction equation to obtain forecasts of the prices in years 7 and 8 .
c. Find $95 \%$ prediction intervals for years 7 and 8 .