11. Correlation

In Exercise 24, remove the data for the student who is 57 inches tall and scored 128 on the IQ test. Describe how this affects the correlation coefficient r.

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

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b. Based on the result from part (a), what do you conclude about a linear correlation between time and height?

[DATA] Buying a New Car How much does the typical person pay for a new 2019 Audi A4? The following data represent the selling price of a random sample of new A4s (in dollars).

d. Verify it is reasonable to conclude that this data come from a population that is normally distributed.

"In studies of monozygotic (identical) twins, the correlation between intelligence (IQ) scores is 0.85.

c. What fraction of the variation in one twin’s IQ can be accounted for by the other twin’s IQ?"

Appendix B Data Sets

In Exercises 29–32, use the data from Appendix B to construct a scatterplot, find the value of the linear correlation coefficient r, and find either the P-value or the critical values of r from Table A-6 using a significance level of α = 0.05. Determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

Taxis Repeat Exercise 15 using all of the time/tip data from the 703 taxi rides listed in Data Set 32 “Taxis” from Appendix B. Compare the results to those found in Exercise 15.

Bull Markets A bull market is defined as a market condition in which the price of a security rises for an extended period of time. A bull market in the stock market is often defined as a condition in which a market rises by 20% or more without a 20% decline. The data to the right represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) during the 25 bull markets dating back to 1929 (the year of the famous market crash).

b. Determine the linear correlation coefficient between months and percent change.