Question

Multiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin, the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was developed to predict the price of wheat using three supply-and-demand explanatory variables.Data for 14 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation. The value of R2was 0.989.
(a) The fitted model gave the predicted value $2.136 with standard error $0.013. Express the prediction as an interval. (The degrees of freedom were large for this analysis, so use 100 as the df to determine t*.)
(b) The actual price for the period in question was $2.13. The judge decided that the analysis provided evidence that the price was not artificially depressed, and the opinion was sustained by the court of appeals. Write a short summary of the results of the analysis that relate to the decision and explain why you agree or disagree with it.

Answer 1

Answer:

($2.123 ; $2.149)

Step-by-step explanation:

The prediction interval is expressed as :

Predicted value ± standard Error

Predicted value = $2.136

Standard Error = $0.013

Prediction interval :

Lower boundary = $2.136 - $0.013 = $2.123

Upper boundary = $2.136 + $0.013 = $2.149

($2.123 ; $2.149)

B.) The prediction interval provides a range for which the predicted value or price should fall Given a certain degree of probability. If the true value falls within this interval, then, our prediction would be deemed to have occurred not by chance.

Since the actual price within the predicted price interval, then I agree with the judge's Decison that the price was not artificially depressed.