Solved: Calories versus Sugar The following data represent the number of calories per

Chapter 14, Problem 20

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Calories versus Sugar The following data represent the number of calories per serving and the number of grams of sugar per serving for a random sample of high-protein and moderate-protein energy bars. Calories, x Sugar, y Calories, x Sugar, y 180 10 270 20 200 18 320 2 210 14 110 10 220 20 180 12 220 0 200 22 230 28 220 24 240 2 230 24 Source: Consumer Reports (a) Draw a scatter diagram of the data, treating calories as the explanatory variable. What type of relation, if any, appears to exist between calories and sugar? (b) Determine the least-squares regression equation from the sample data. (c) Compute the standard error of the estimate. (d) Determine whether the residuals are normally distributed. (e) Determine sb1 . (f) If the residuals are normally distributed, test whether a linear relation exists between calories and sugar content at the a = 0.01 level of significance. (g) If the residuals are normally distributed, construct a 95% confidence interval about the slope of the true least-squares regression line. (h) For a randomly selected energy bar, would you recommend using the least-squares regression line obtained in part (b) to predict the sugar content of the energy bar? Why? What would be a good estimate for the sugar content of the energy bar?