One desirable dietary change if you want to "eat right," is to reduce the intake of red meat and to substitute poultry or fish. Researchers tracked beef and chicken consumption, y (in annual pounds per person), and found the consumption of beef declining and the consumption of chicken increasing over a period of 7 years. A summary of their data is shown in the table.

Consider fitting the following model, which allows for simultaneously fitting two simple linear regression lines:
E(y) = β0 + β1x1 + β2x2 + β3x1x2
where y is the annual meat (either beef or chicken) consumption per person per year,

MINITAB output for Exercise 13.20
Regression Analysis: y versus x1, x2, x1x2
The regression equation is
y = 23.6 + 69.0 x1 + 7.75 x2 - 12.3 x1x2
Question continue over next page

Diagnostic plots for Exercise 13.20

Question continue over next page

a. How well does the model fit? Use any relevant statistics and diagnostic tools from the printout to answer this question.
b. Write the equations of the two straight lines that describe the trend in consumption over the period of 7 years for beef and for chicken.
c. Use the prediction equation to find a point estimate of the average per-person beef consumption in year 8. Compare this value with the value labeled "Fit" in the printout.
d. Use the printout to find a 95% confidence interval for the average per-person beef consumption in year 8. What is the 95% prediction interval for the per person beef consumption in year 8? Is there any problem with the validity of the 95% confidence level for these intervals?

Transcribed Image Text:

h-7677249 C-3344677 9668 1 2 3 4 5 6 7 1 if beef 0 if chicken and X2=Year Xi= 1 Predictor Constant xl X2 x1x2 Coef 23.571 69.000 7.7500 -12.286 SE Coef 3.522 4.981 0.7875 1.114 6.69 0.000 13.85 0.000 9.84 0.000 -11.03 0.000 S=4.16705 R-Sq 95.4% R-Sq(adj ) 94.1 = Analysis of Variance Source Regression Residual Error 10 Total DF MS 3 3637.9 1212.6 69.83 0.000 17.4 173.6 13 3811.5 Seq ss 1380.1 Source x1 X2 xlx2 DF 144.6 2113.1 predicted Values for New Observations New Obs 1 56.29 3.52 (48.44, 64.13) (44.13, 68. 44) Fit SE Fit 95% CI 95% PI Values of Predictors for New observations New Obs x1 1.00 X2 8.00 XIX2 8.00 Normal Probability Plot of the Residuals (res ponse is y 99-- 95 90 80 70 50 5 10 10 Residual Residuals versus the Fitted Values fresponse is y 5.0 2.5- 0.0 -5.0 30 40 50 60 Fitted Value 70 80 90