Consider estimation of a short$-$run average variable cost function of the form

AVC $=$ a $+$ bQ $+$ cQ$2$

Using time$-$series data, the estimation procedure produces the following computer output: $[8$ Points$]$

a$.$ Do the parameter estimates have the correct signs? Are they statistically significant at the $5$ percent level of significance? $-1$ Point

b$.$ At what level of output do you estimate average variable cost reaches its minimum value? $-1$ Point

c$.$ What is the estimated marginal cost curve? $-2$ Points

d$.$ What is the estimated marginal cost when output is $1,000$ units? $-1$ Point

e$.$ What is the estimated average variable cost curve? $-1$ Point

f$.$ What is the estimated average variable cost when output is $1,000$ units? $-2$ Points