(Situation O) Using Data from the Post-Korean War Period, an Economist

(Situation O) Using data from the post-Korean war period, an economist modeled annual consumption, $y _ { t }$ as a function of total labor income, $\mathrm { x } _ { 1 } \mathrm { t }$ , and total property income, $\mathrm { x } _ { 2 } \mathrm { t }$ , with the following results. Assume data for $\mathrm { n } = 40 \mathrm { years }$ were used in the analysis.
$$\hat { y } _ { t } = 7.81 + 0.91 x _ { 1 t } + 0.57 x _ { 2 t } \quad s = 1.29 \quad \text { Durbin-Watson } d = 2.09$$
-For the situation above, set up the null and alternative hypotheses for testing for the presence of autocorrelation of residuals.

A) $\mathrm { H } _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0$
$\mathrm { H } _ { \mathrm { a } }$ : At least one $\beta \neq 0$

B) $\mathrm { H } _ { 0 }$ : No first-order autocorrelation
$\mathrm { H } _ { \mathrm { a } }$ : Negative first-order autocorrelation

C) $\mathrm { H } _ { 0 }$ : No first-order autocorrelation
$\mathrm { H } _ { \mathrm { a } }$ : Positive or Negative first-order autocorrelation

D) $\mathrm { H } _ { 0 }$ : No first-order autocorrelation
$\mathrm { H } _ { \mathrm { a } }$ : Positive first-order autocorrelation