The amounts of sugar (grams of sugar per 1 cup serving of cereal) and calories (

Question

The amounts of sugar (grams of sugar per 1 cup serving of cereal) and calories (per 1 cup serving of cereal) for six randomly selected breakfast cereals was obtained from the website http: //www.acaloriecounter.com/breakfast-cereal.php. Data follows: The mean of the 6 amounts of sugar is 12.3 grams, with a sample standard deviation of 5.888. The mean of the 6 calorie counts is 135, with a sample standard deviation of 33.317. a. Using your answers to Question (11): are there any outliers in the data? Use the Outlier Test to determine the answer: if there is/are outlier(s) in the data, identify it/them. Explain how your determination was made. b. Using your answers to Question (11): calculate the coefficient of determination r^2 c. What is the numerical percent of variation in "calories per 1 cup serving" variable that CANNOT be explained by the variation in the "grams sugar per 1 cup serving" variable?

Explanation / Answer

Ans:

b)Correlation cofficient=r=

=(6*10720-74*810)/(SQRT(6*1086-74^2)*SQRT(6*114900-810^2))

=0.74

Cofficient of detremination=r2=0.742

r2=0.55

c)Cofficient of determination indicate the percent of the variation of dependent variable(calories per 1 cup serving) can be explained by the variation in independent variable(grams sugar per 1 cup serving).

r2=0.55

Cofficient of non -detrmination=1-r2=1-0.55=0.45

45% of the variation of "calories per 1 cup serving" can not be explained by the variation in "grams sugar per 1 cup serving".

x y xy x^2 y^2 1 13 120 1560 169 14400 2 12 160 1920 144 25600 3 15 120 1800 225 14400 4 2 100 200 4 10000 5 20 190 3800 400 36100 6 12 120 1440 144 14400 Total 74 810 10720 1086 114900

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