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Chapter 3: Q 49. (page 204)

Actual weight Refer to Exercise 47. Use the equation of the least-squares regression line and the residual plot to estimate the actual mean weight of the infants when they were 1 month old.

Short Answer

Expert verified

The shape of the image is approximately normally distributed.

Step by step solution

01

Given information

The figure is

02

Concept

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

03

Explanation

In a survey, 400 respondents were asked to affix a blue sticker next to the oldest person they have ever known on a large wall.

The sample size is huge, therefore (more than 30). As a result, the image's shape is roughly and normally distributed.

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Most popular questions from this chapter

Longer strides In Exercise 43, we summarized the relationship between x =

height of a student (in inches) and y = number of steps required to walk the length of a school hallway, with the regression line y^=113.6−0.921x. For this

model, technology gives s = 3.50 and r2 = 0.399.

a. Interpret the value of s.

b. Interpret the value of r2.

The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable x to be the percent change in a stock market index in January and the response variable y to be the change in the index for the entire year. We expect a positive correlation between x and y because the change during January contributes to the full year’s change. Calculation from data for an 18-year period gives x¯=1.75% sx=5.36% y¯=9.07% sy=15.35% r=0.596

a. Find the equation of the least-squares line for predicting full-year change from January change.

b. Suppose that the percent change in a particular January was 2 standard deviations above average. Predict the percent change for the entire year without using the least-squares line.

What’s my grade? In Professor Friedman’s economics course, the correlation

between the students’ total scores prior to the final examination and their final exam scores is r = 0.6. The pre-exam totals for all students in the course have a mean of 280 and a standard deviation of 30. The final exam scores have a mean of 75 and a standard deviation of 8. Professor Friedman has lost Julie’s final exam but knows that her total before the exam was 300. He decides to predict her final exam score from her pre-exam total.

a. Find the equation for the least-squares regression line Professor Friedman should use to make this prediction.

b. Use the least-squares regression line to predict Julie’s final exam score.

c. Explain the meaning of the phrase “least squares” in the context of this question.

d. Julie doesn’t think this method accurately predicts how well she did on the final exam. Determine r2. Use this result to argue that her actual score could have been much higher (or much lower) than the predicted value.

Fruit fly thorax lengths (2.2) Fruit flies are used frequently in genetic research because of their quick reproductive cycle. The length of the thorax (in millimeters) for male fruit flies is approximately Normally distributed with a mean of 0.80 mm and a standard deviation of 0.08 mm.21

a. What proportion of male fruit flies have a thorax length greater than 1 mm?

b. What is the 30th percentile for male fruit fly thorax lengths?

Sarah’s parents are concerned that she seems short for her age. Their doctor has kept the following record of Sarah’s height:

a. Make a scatterplot of these data using age as the explanatory variable. Describe what you see.

b. Using your calculator, find the equation of the least-squares regression line.

c. Calculate and interpret the residual for the point when Sarah was 48 months old.

d. Would you be confident using the equation from part (b) to predict Sarah’s height when she is 40 years old? Explain.
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