Fish sizes. Use explanatory variables length, width, and interaction from Exercise 28.25 (page 28-52) on the 56 perch to provide 95% confidence intervals for the mean and prediction intervals for future observations. Interpret both intervals for the 10th perch in the data set. What t distribution is used to provide both intervals?
Exercise 28.25:
25 Fish sizes. Table 28.8 contains data on the size of perch caught in a lake in Finland.10 Use statistical software to help you analyze these data.
(a) Use the multiple regression model with two explanatory variables, length and width, to predict the weight of a perch. Provide the estimated multiple regression equation.
(b) How much of the variation in the weight of perch is explained by the model in part (a)?
(c) Does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch? Explain.
(d) Do the individual t tests indicate that both ß1 and ß2 are significantly different from zero? Explain.
(e) Create a new variable, called interaction, that is the product of length and width. Use the multiple regression model with three explanatory variables, length, width, and interaction, to predict the weight of a perch. Provide the estimated multiple regression equation.
(f) How much of the variation in the weight of perch is explained by the model in part (e)?
(g) Does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch? Explain.
(h) Describe how the individual t statistics changed when the interaction term was added.