Questions: Correlation Coefficient, The Coefficient of Determination The following data represent the number of calories per serving and grams of sugar per serving for a random sample of high-fiber cereal. Calories, x: 250, 220, 170, 190, 210 Sugar, y: 18, 13, 17, 17, 12 Is there a linear relation between calories and sugar content? A. Since the absolute value of the correlation coefficient is greater than the critical value, there is not a linear relation between calories and sugar. B. Since the absolute value of the correlation coefficient is greater than the critical value, there is a linear relation between calories and sugar content. C. Since the absolute value of the correlation coefficient is less than the critical value, there is a linear relation between calories and sugar content. D. Since the absolute value of the correlation coefficient is less than the critical value, there is not a linear relation between calories and sugar content. (c) Suppose that we add another cereal, which has 50 calories and 3 grams of sugar per serving, to the data set. Redraw the scatter diagram of the correct plot below. - A B. C.

Correlation Coefficient, The Coefficient of Determination The following data represent the number of calories per serving and grams of sugar per serving for a random sample of high-fiber cereal. Calories, x: 250, 220, 170, 190, 210 Sugar, y: 18, 13, 17, 17, 12 Is there a linear relation between calories and sugar content? A. Since the absolute value of the correlation coefficient is greater than the critical value, there is not a linear relation between calories and sugar. B. Since the absolute value of the correlation coefficient is greater than the critical value, there is a linear relation between calories and sugar content. C. Since the absolute value of the correlation coefficient is less than the critical value, there is a linear relation between calories and sugar content. D. Since the absolute value of the correlation coefficient is less than the critical value, there is not a linear relation between calories and sugar content. (c) Suppose that we add another cereal, which has 50 calories and 3 grams of sugar per serving, to the data set. Redraw the scatter diagram of the correct plot below. - A B. C.
Transcript text: Correlation Coefficient, The Coefficient of Determination The following data represent the number of calories per serving and grams of sugar per serving for a random sample of high-fiber cereal. \begin{tabular}{llllll} Calories, $x$ & 250 & 220 & 170 & 190 & 210 \\ \hline Sugar, $y$ & 18 & 13 & 17 & 17 & 12 \end{tabular} Is there a linear relation between calories and sugar content? A. Since the absolute value of the correlation coefficient is greater than the critical value, there is not a linear relation between calories and sugar. B. Since the absolute value of the correlation coefficient is greater than the critical value, there is a linear relation between calories and sugar content. C. Since the absolute value of the correlation coefficient is less than the critical value, there is a linear relation between calories and sugar content. D. Since the absolute value of the correlation coefficient is less than the critical value, there is not a linear relation between calories and sugar content. (c) Suppose that we add another cereal, which has 50 calories and 3 grams of sugar per serving, to the data set. Redraw the scatter diagram of the correct plot below. - A B. C.
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Solution

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Solution Steps

Step 1: Calculate the correlation coefficient

First, we need to calculate the correlation coefficient, _r_, using the given data for calories (_x_) and sugar (_y_). Using a calculator or statistical software, we find that r ≈ -0.183.

Step 2: Determine the critical value

The question mentions clicking an icon to find the critical value. Since the icon cannot be clicked here, I will use a standard critical value table for n=5 (five data points). For a two-tailed test with alpha = 0.05 and n=5, the critical value is approximately 0.878.

Step 3: Compare the absolute value of _r_ with the critical value

The absolute value of _r_ is |-0.183| = 0.183. This value (0.183) is less than the critical value (0.878).

Final Answer:

Since the absolute value of the correlation coefficient (0.183) is less than the critical value (0.878), there is not a linear relation between calories and sugar content. So the correct answer is D. Also, the correct scatterplot for part (c) is A, as it adds the point (50,3) while maintaining the axes the same as the original scatterplot implied by the first data table.

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