Consider the Monthly Time Series Shown in the Table A Use the Method of Least Squares to Fit the {\text

Essay

Consider the monthly time series shown in the table. $\begin{array}{l|c|c}\hline {\text { Month }} & \mathrm{t} & \mathrm{Y} \\\hline \text { January } & 1 & 185 \\\hline \text { February } & 2 & 192 \\\hline \text { March } & 3 & 189 \\\hline \text { April } & 4 & 201 \\\hline \text { May } & 5 & 195 \\\hline \text { June } & 6 & 199 \\\hline \text { July } & 7 & 206 \\\hline \text { August } & 8 & 203 \\\hline \text { September } & 9 & 208 \\\hline \text { October } & 10 & 209 \\\hline \text { November } & 11 & 218 \\\hline \text { December } & 12 & 216 \\\hline\end{array}$

a. Use the method of least squares to fit the model $\mathrm { E } \left( \mathrm { Y } _ { \mathrm { t } } \right) = \beta _ { 0 } + \beta _ { 1 } \mathrm { t }$ to the data. Write the prediction equation.
b. Construct a residual plot for the model.
c. Is there evidence of a cyclical component? Explain.