EXAMINING RELATIONSHIPS CHECKPOINT 2
What can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data?
r and b have the same sign (+ or -)
A study was done on the batting averages for two baseball players: Hitmore and Bunter. Data were collected over a period of time for baseball parks that are natural and artificial turf. It was found that Hitmore does better overall (i.e., has a better batting average). However, for both natural and artificial turf separately, Bunter does better. Which of the following is correct?
Both (B) and (C) are correct.
A researcher is conducting a study and you are hired to help them analyse their data. They have already looked at scatterplots and they give you only the linear correlation coefficient to consider. Suppose a correlation of r = .87 is found between sunscreen sales and number of drownings over a 1-year period. Based on this information given, what would you advise?
Both (B) and (C) are true.
A local ice cream shop kept track of the number of cans of cold soda it sold each day, and the temperature that day, for two months during the summer. The data are displayed in the scatterplot below: The X-axis is temperature measured in degrees Fahrenheit with a range from about 55 to 100 degrees. The Y-axis is the number of cans of soda sold with a range from about 165 to 195 cans. The points begin in the lower left, end in the upper right, and follow a fairly linear pattern. One point is away from the others in the lower right portion of the graph. The one outlier corresponds to a day on which the refrigerator for the soda was broken. Which of the following is true?
If the outlier were removed, r would get closer to 1
The data in the scatterplot below are an individual's weight and the time it takes (in seconds) on a treadmill to raise his or her pulse rate to 140 beats per minute. The o's correspond to females and the +'s to males. Which of the following conclusions is most accurate? The X-axis is Weights with a range from about 90 to 180 pounds. The Y-axis is Time with a range from about 115 to 165 seconds. The points with o's begin in the upper left, end in the lower middle, and follow a fairly linear pattern. the points with +'s begin in the upper middle, end in the lower right, and follow a fairly linear pattern.
There is a negative correlation between time and weight for males and for females.
A researcher is conducting a study and you are hired to help them analyse their data. They have already looked at scatterplots and they give you only the linear correlation coefficient to consider. Suppose that the correlation r between two quantitative variables was found to be r = 0. Based only on the information given, what would you advise?
There is no linear relationship between the two variables.
Heart attacks cause many deaths. Researchers in the Physicians Health Study (1989) gave a large sample of healthy male physicians either a low dose of aspirin or a placebo. The following two-way table gives the results of the study: Heart Attack? Yes No Total Medication Aspirin 139 10,898 11,037 Placebo 239 10,795 11,034 Total 378 21,693 22,071 In this example, it would be appropriate to calculate:
conditional row percentages
