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Chapter 3: Q 16. (page 173)

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.

Short Answer

Expert verified

There is a weak and positive association between the count of crying peaks and IQ at age 3 years.

Step by step solution

01

Given information

Correlation, r=0.45

02

Explanation

A positive linear correlation exists when r is positive.

A negative linear correlation exists when r is negative.

For weak correlation,

For moderate correlation,

For strong correlation,

Note that

The association between the crying of infants 4 to 10 days old and their IQ test scores at the age of 3 years is a weak and positive association.

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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.

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 “least-squares” regression line.

Actual consumption Refer to Exercise 48. Use the equation of the least-squares regression line and the residual plot to estimate the actual fuel consumption of the car when driving 20 kilometers per hour.

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 = 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. Show your work.

(b) The mean change in January is x=1.75%. Use your regression line to predict the change in the index in a year in which the index rises1.75% in January. Why could you have given this result (up to roundoff error) without doing the calculation?

If we leave out the low outlier, the correlation for the remaining 13 points in the preceding figure is closest to

a. −0.95.

b. −0.65.

c. 0.

d. 0.65.

e. 0.95.
See all solutions

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