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Chapter 3: Q 51. (page 204)

Movie candy Is there a relationship between the amount of sugar (in grams) and the number of calories in movie-theater candy? Here are the data from a sample of 12 types of candy:

a. Sketch a scatterplot of the data using sugar as the explanatory variable.

b. Use technology to calculate the equation of the least-squares regression line for predicting the number of calories based on the amount of sugar. Add the line to the scatterplot from part (a).

c. Explain why the line calculated in part (b) is called the 鈥渓east-squares鈥� regression line.

Short Answer

Expert verified

Part (b) The regression line is: y铃�=2.829x+300.040

Part (c) It's known as a least square regression line.

Part (a)

Step by step solution

01

Part (a) Step 1: Given information

The data set is

02

Part (a) Step 2: Concept

The least-squares regression line reduces the sum of squares of vertical distances between the observed points and the line to zero.

03

Part (a) Step 3: Explanation

The scatter plot is:

04

Part (b) Step 1: Explanation

The output obtained using the Ti-83 calculator is:

Thus, the regression line is: y铃�=2.829x+300.040

The regression line on the scatter plot could be shown as:

05

Part (c) Step 1: Explanation

Because it is a regression line, the regression line generated in the previous section minimizes the errors or residuals. As a result, it's known as a least square regression line.

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Most popular questions from this chapter

In a scatterplot of the average price of a barrel of oil and the average retail price of a gallon of gas, you expect to see

a. very little association.

b. a weak negative association.

c. a strong negative association.

d. a weak positive association.

e. a strong positive association.

More crying? Refer to Exercise 16Does the fact that r=0.45 suggest that making an infant cry will increase his or her IQ later in life? Explain your reasoning.

More candy Refer to Exercise 51. Use technology to create a residual plot. Sketch the residual plot and explain what information it provides.

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c. It makes the correlation equal to 0.

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Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled 鈥淔itted value,鈥� which means the same thing as 鈥減redicted value.鈥�

What was the actual activity level rating for the fish at a temperature of 20掳C?

a. 87

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d. 66

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