Question

Statistics 11 Homework 9 Due Wednesday, Nov. 20 Metals.jmp lists the yearly average price of gold, copper, silver, and aluminum. We wish to predict the price of gold. 1. Create a correlation matrix of all four variables. Based on the correlation coefficients, how can you tell that it is reasonable to include all of the predictors (copper, silver, and aluminum) in the model? Explain briefly. 2. Fit a first-order multiple regression model using all three predictors and report the prediction function. 3. Use your prediction function to predict the price of gold when copper's price is 70 cents/lb, silver's price is $10/oz, and aluminum's price is 80 cents/lb. 4. Perform a Shapiro-Wilk test on the errors/residuals. Based on your result, is it reasonable to assume that the population errors/residuals are normally distributed? 5. Plot the residuals against each predictor variable. Based on your results, is it reasonable to assume a linear relationship between Y and each X? Explain briefly how the patterns on the plots help you decide. 6. Is it reasonable to assume that the errors have constant variance? Name the plot and pattern you used to decide. 7. Interpret the value of se in a sentence. 8. Write a set of hypotheses to test that the overall regression model is useful at predicting the price of gold. Provide two versions: symbols and words. 9. Report the test statistic and P-value for the test described in question 8. Then interpret/summarize the findings of this test in one sentence, using a = 0.05. 10. Write a set of hypotheses to test that the price of copper, in conjunction with the prices of silver and aluminum, is useful in predicting the price of gold. Provide two versions: symbols and words. 11. Report the test statistic and P-value for the test described in question 10. Then interpret/summarize the findings of this test in one sentence, using a -0.05. 12. Find and interpret a 95% confidence interval for silver's ß coefficient. 13. Interpret Rand the adjusted in a sentence (you can cover both in the same sentence). 14. The adjusted R is farther away from R than it was in the examples we covered in class so far. Why do you suppose that is? Hint: consider how n compares to k. 15. Consider your results to questions 11, 12, and 14. Eliminate one of the predictors to produce a simpler, more efficient multiple regression model that predicts the price of gold. Report your prediction function. 16. Which model do you think is better: the model from question 2 or the model from question 15? Compare/contrast the values of S, R, and adjusted R to support your choice.

gold ($/oz) Y	copper (cents/lb) X1	silver ($/oz) X2	Aluminum (cents/lb) X3
161.1	64.2	4.4	39.8
308	93.3	11.1	61
613	101.3	20.6	71.6
460	84.2	10.5	76
376	72.8	8	76
424	76.5	11.4	77.8
361	66.8	8.1	81
318	67	6.1	81
368	66.1	5.5	81
448	82.5	7	72.3
438	120.5	6.5	110.1
382.6	130.9	5.5	87.8

Answer 1

1)

Using Excel

data -> data analysis -> correlation

we see that copper and aluminum are moderately correlation , silver is strongly correlated

we can include all variable

2)

Using Excel

data -> data analysis -> regression

Gold^ = -51.5749 + 0.0696 copper + 18.7835 silver + 3.5378 aluminum

3)
Gold^ = -51.5749 + 0.0696 * 70 + 18.7835 *10 + 3.5378 * 80
= 424.1561

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