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Chapter 3: Q 18. (page 173)

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.

Short Answer

Expert verified

No.

Step by step solution

01

Given information

02

Explanation

From Exercise 16it is known there exists a weak correlation between the two variables.

The correlation is a statistical measure that is used to explain the relationship between two variables.

The exercise's association reveals a weak relationship between the variables count of crying peaks and an infant's IQat the age of three. Because correlation does not necessarily imply causation.

Thus,

r=0.45does not imply that making an infant cry will lead an increase in her or his IQ in later life.

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Most popular questions from this chapter

Late bloomers? Japanese cherry trees tend to blossom early when spring weather is warm and later when spring weather is cool. Here are some data on the average March temperature (in degrees Celsius) and the day in April when the first cherry blossom appeared over a 24-year period:

a. Make a well-labeled scatterplot that’s suitable for predicting when the cherry trees will blossom from the temperature. Which variable did you choose as the explanatory variable? Explain your reasoning.

b. Use technology to calculate the correlation and the equation of the least-squares regression line. Interpret the slope and y-intercept of the line in this setting.

c. Suppose that the average March temperature this year was 8.2°C. Would you be willing to use the equation in part (b) to predict the date of the first blossom? Explain your reasoning.

d. Calculate and interpret the residual for the year when the average March temperature was 4.5°C.

e. Use technology to help construct a residual plot. Describe what you see.

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 xto be the percent change in a stock market index in January and the response variable yto be the change in the index for the entire year. We expect a positive correlation between xand 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%sz=5.36%y¯=9.07%sy=15.35%r=0.596

(a) What percent of the observed variation in yearly changes in the index is explained by a straight-line relationship with the change during January?

(b) For these data, s=8.3Explain what this value means

Which of the following is not a characteristic of the least-squares regression line?

a. The slope of the least-squares regression line is always between –1 and 1.

b. The least-squares regression line always goes through the point (x¯,y¯) .

c. The least-squares regression line minimizes the sum of squared residuals.

d. The slope of the least-squares regression line will always have the same sign as the correlation.

e. The least-squares regression line is not resistant to outliers.

It’s still early We expect that a baseball player who has a high batting average in the first month of the season will also have a high batting average for the rest of the season. Using 66 Major League Baseball players from a recent season,33 a least-squares regression line was calculated to predict rest-of-season batting average y from first-month batting average x. Note: A player’s batting average is the proportion of times at-bat that he gets a hit. A batting average over 0.300 is considered very good in Major League Baseball.

a. State the equation of the least-squares regression line if each player had the same batting average the rest of the season as he did in the first month of the season.

b. The actual equation of the least-squares regression line is y^=0.245+0.109x

Predict the rest-of-season batting average for a player who had a 0.200 batting average the first month of the season and for a player who had a 0.400 batting average the first month of the season.

c. Explain how your answers to part (b) illustrate regression to the mean.

Oh, that smarts! Infants who cry easily may be more easily stimulated than others. This may be a sign of a higher IQ. Child development researchers explored the relationship between the crying of infants 4 to 10 days old and their IQ test scores at age 3 years. A snap of a rubber band on the sole of the foot caused the infants to cry. The researchers recorded the crying and measured its intensity by the number of peaks in the most active 20 seconds. The correlation for these data is r=0.45.16 Interpret the correlation.
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