(1) Hypothesis: $H_0: R^2 = 0$ , formally $\beta_2 = \beta_3 = 0$ , $H_1: R^2 > 0$ , formally at least one $\beta_1 \neq 0$ , $p = 3,3$

(2) $\alpha = 0,05$

(3) $R^2_{HR}, R^2_{R}, \beta_2, \beta_3$

(4) Assumptions: $\cos(\kappa_{ij}, \mu_i) = 0$ for all $j$ .
No exact multicollinearity
$\mu_i \sim N(0/0, \sigma^2)$

(5)
$F_{0,05} = \frac{(R^2_{HR} - R^2_{R}) / m}{(1 - R^2_{HR}) / (n - k)} \sim F_{m,n-k}$

Respected model: $c = \mu_i + \mu_i$
Unrespected model: $c = \mu_i = \beta_1 + \beta_2 + \mu_i + \beta_3$ prime, i.e.
$m = \text{must of restriction} = 2$
$n = \text{must of obs.} = 72$
$k = \text{must of prime in } HR \text{ model} = 3$

\left\{ \begin{array}{l} V_1 = m = 2 \\ V_2 = 89 - \text{rounded} \\ \text{down to 60} \\ \text{to find in table} \end{array} \right.

E)

Reject

H_0

if

F_{0,05} > 3,15

(6)

F_{0,05} = \frac{(0,007777 - 0) / 2}{(1 - 0,007777) / (7^2 - 3)} = 0,08011 \sim 0,08011

F_{0,05} = 0,08 < 3,15

Since

F_{0,05}

is not in the rejection region we can't reject the

H_0

that

\beta_2 = \beta_3 = 0

in favor of the alternate hypothesis