Exercise 9.41 gives output for a regression model to predict calories in a serving of breakfast cereal based on the number of grams of fiber in the serving. Use this output, together with any helpful summary statistics from Table 9.3, to show how to calculate the following regression quantities.

Table 9.3

(a) The standard deviation of the error term, s_Ñ”.
(b) The standard error of the slope, SE.

Exercise 9.41

In Data 9.2 on page 540, we introduce the dataset Cereal, which has nutrition information on 30 breakfast cereals. Computer output is shown for a linear model to predict Calories in one cup of cereal based on the number of grams of Fiber. Is the linear model effective at predicting the number of calories in a cup of cereal? Give the F-statistic from the ANOVA table, the p-value, and state the conclusion in context.

In Data 9.2 on page 540

Labels on many food products contain a wealth of nutritional information. The data in Cereal include the number of calories as well as the grams of fat, carbohydrates, fiber, sugars, and protein and milligrams of sodium in each cup of a sample of 30 breakfast cereals from three different manufacturers (General Mills, Kellogg€™s, and Quaker).

Sample Size 30 Mean Std.Dev. Calories Fiber 133.83 34.812 1.880 30 1.797 The regression equation is Calories = 119 + 8.48 Fiber Source Regression Analysis of Variance DF 1 MS 7.44 7376.1 27774.1 35150.2 7376.1 991.9 0.011 Residual Error 28 29 Total