The yield is given by the regression equation
y = 859 + 5.76x₁ + 3.82x₂
where
x₁ = number of acres planted
x₂ = number of acres harvested
The goodness of fit is r² = 0.94.
This appears to a very good fit to the data because it is almost equal to 1.
To assess the goodness of fit in a statistical sense, it may also necessary to perform an F-test in a hypothesis test. This is not possible without having raw measured data.
For this problem, r²=0.94 may be considered to be a very good fit to the measured data.
Part a.
When x₁ = 3200 acres and x₂ = 3000 acres, obtain
y = 859 + 5.76*3200 + 3.82*3000
= 30,751 pounds
Part b.
Without performing a hypothesis test or a residual plot, we can conclude that the predicted value is in very good agreement with the actual value.
Because we do not have raw measured data, we can neither plot the residuals nor perform a hypothesis test.
In general,
When r² = 1, the agreement is exact.
When r² = 0, there is absolutely no agreement.
A value of r² > 0.9 is considered good.
Critical points occur where the gradient is zero. This is guaranteed whenever
and either
or
.
The Hessian matrix for this function looks like
and has determinant
Maxima occur whenever the determinant is positive and
. Minima occur whenever both the determinant and
are positive. Saddle points occur whenever the determinant is negative.
At
, you have a saddle point since the determinant reduces to -324, so
is the saddle point.
At
, the determinant is
and
, so
is a local maximum.
No other critical points remain, so you're done.
The function that models the scenario is
v = init_v + acceleration * time
Plug the values into the equation,
0 = 28 + a * 7 => -28 = a * 7 => a = - 28/7 m/s.
1) 3/4-1/4=2/4=1/2
2)3/10-1/10=2/10=1/5
Volume of cylinder = Base Area x Height
Height = Volume/Base
Height = (6n² -13n -28)/(3n+4)
Perform this division and you will get Height = 2n-7
