Question

6. To predict the annual rice yield in pounds we use the equation y-hat = 859 + 5.76x1 + 3.82x2 where x1 represents the number of acres planted and where x2 represents the number of acres harvested and where r2 = 0.94.
a. Predict the annual yield when 3200 acres are planted and 3000 are harvested 19291+11460=30751

b. Interpret the results of r2 value. THIS IS WHAT I DON'T UNDERSTAND. THANKS.

Answer 1

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.