Measuring the Strength of Linear Associations with a Correlation Coefficient

  • 1.

    An air quality analyst measured the average wind speeds (taken at 7:00 a.m. and 10:00 a.m.) at an airport for a week (seven days). The correlation coefficient between day number and average wind speed for this particular dataset is r = -0.13. Which of the following best describes the strength of this linear correlation?

    Answers:

    • negligible and positive

    • moderate and negative

    • moderate and positive

    • negligible and negative

  • 2.

    A nuclear scientist studying the decay of a highly radioactive substance noted that the correlation coefficient between the amount of the substance remaining at time {eq}x {/eq} and time {eq}x {/eq} is r = -0.01. Which of the following statements is/are always true based on this computed value of r?

    I. The strength of the linear correlation between the amount of substance remaining and time is extremely strong and negative.

    II. The strength of the linear correlation between the amount of substance remaining and time is negligible.

    III. The strength of the linear association between these two variables is negative.

    Answers:

    • II and III only

    • I and II only

    • II only

    • I, II, and III

  • 3.

    A woman who is interested in measuring the association between height and weight among female citizens of a certain country obtained an estimate of r = 0.9955 based on a dataset gathered for this purpose. This association is _____.

    Answers:

    • weak and negative

    • extremely strong and negative

    • weak and positive

    • extremely strong and positive

  • 4.

    The coefficient of linear correlation between a company's first-quarter sales from 1941-1950 and its first-quarter sales 40 years later, i.e., from 1981-1990, is r = -0.12. The strength of the linear association between these two variables is best described as a _____.

    Answers:

    • weak and negative linear correlation

    • weak and positive linear correlation

    • negligible and positive linear correlation

    • negligible and negative linear correlation

  • 5.

    A plant geneticist noted that the coefficient of linear correlation between petal lengths and sepal widths in Iris setosa, a certain species of the iris flower, is r = 0.18, based on a sample obtained for this purpose. Which of the statement/s below is/are always true based on this computed value for r?

    I. The strength of the linear correlation between the petal length and sepal width in Iris setosa is extremely strong.

    II. The strength of the linear correlation between these two variables is negligible.

    III. The strength of the linear association between these two variables is positive.

    IV. The strength of the linear association between these two variables is negative.

    Answers:

    • II and III only

    • I, II, and IV only

    • I, II, and III only

    • I and II only

  • 6.

    A scientist observed that for a certain plant species under certain conditions, the coefficient of linear correlation between the ambient carbon dioxide concentration (in mL/L) and rate of carbon dioxide uptake (in μmol/m²/s) is equal to 0.56. Which of the following best describes the linear association between these two variables of interest?

    Answers:

    • moderate and negative

    • weak and negative

    • weak and positive

    • moderate and positive

  • 7.

    A taxonomist obtained a sample of a certain species of the iris (Iris virginica). The correlation coefficient between the sepal width and petal length of the flowers in his sample is r = 0.40. The strength of the linear correlation between these two variables is _____.

    Answers:

    • moderate and positive

    • weak and positive

    • weak and negative

    • moderate and negative

  • 8.

    A senior high school student conducted a mini-survey to determine if the desire to join a basketball varsity team is associated with height among the male members of his peers. The scale for measuring desire that John used in his mini-survey assigns more positive ratings to stronger desires. He obtained a coefficient of linear correlation of r = 0.96. Which of the following best qualifies this association?

    Answers:

    • very strong and negative linear correlation

    • weak and positive linear correlation

    • very strong and positive linear correlation

    • weak and negative linear correlation

  • 9.

    In a recent study, a group of medical researchers reported a correlation coefficient of r = 0.75 between percent body fat (%BF) and body mass index (BMI). Based on this value of r, which of the following best qualifies the strength of this association?

    Answers:

    • strong and positive linear correlation

    • strong and negative linear correlation

    • weak and positive linear correlation

    • weak and negative linear correlation

  • 10.

    To study how Indomethacin is used by the human body, a physiologist measured the Indomethacin concentration every hour for eleven hours in a certain human subject. The coefficient of correlation between these two variables that she obtained based on the data she collected is r = -0.65. What can be said about the strength of the linear correlation between these two variables?

    Answers:

    • moderate and negative

    • weak and positive

    • weak and negative

    • moderate and positive

  • 11.

    A medical researcher noted that the coefficient of correlation between the dose levels of Vitamin C (from ascorbic acid) and lengths of tooth-growth factors among rats is r = 0.89. Describe the strength of this association.

    Answers:

    • weak and negative linear correlation

    • strong and positive linear correlation

    • strong and negative linear correlation

    • weak and positive linear correlation

  • 12.

    John is interested in the association between the height and weight of adult males in his country. Using a sample from reliable census data, he obtained an estimate of r = 0.85. Which of the following best qualifies this linear association?

    Answers:

    • weak and negative

    • strong and positive

    • strong and negative

    • weak and positive

  • 13.

    The coefficient of linear correlation between logarithm (base 10) of the revenue passenger miles and integer year from 1937 to 1960 in the US is r = 0.98. This association is said to be _____.

    Answers:

    • extremely strong and negative

    • weak and positive

    • extremely strong and positive

    • weak and negative

  • 14.

    Find from among the following choices, the best description of the strength of the linear correlation between the petal length and sepal length of a certain iris plant species (Iris setosa) if r = 0.23.

    Answers:

    • negligible and negative

    • moderate and positive

    • negligible and positive

    • moderate and negative

  • 15.

    A pathologist is testing the effect of a very strong antiseptic on a certain strain of bacterium. He noted that the coefficient of linear correlation between the population size of the bacteria measured at selected times (in sec) with the time equals r = -0.41. Based on this value for r, which of the statement/s below is/are always true?

    I. The strength of the linear correlation between the number of virus present and time is extremely strong.

    II. The strength of the linear correlation between these two variables is weak or low.

    III. The strength of the linear association between these two variables is negative.

    IV. The strength of the linear association between these two variables is positive.

    Answers:

    • II only

    • I, II, and III

    • II and III only

    • I and II only

  • 16.

    A financial analyst obtained the coefficient of linear correlation between the revenue passenger miles and integer year from 1937 to 1960 in the US and obtained r = 0.95. Which of the following best describes this association?

    Answers:

    • weak and negative

    • extremely strong and positive

    • weak and positive

    • extremely strong and negative

  • 17.

    The coefficient of linear correlation between integer year and the number of telephones in the world based on a certain data set covering the years 1951-1961 is r = 0.96. Which of the following describes this correlation?

    Answers:

    • extremely strong and positive

    • strong and positive

    • extremely strong and negative

    • strong and negative

  • 18.

    For a dataset gathered to study radioactive decay, a nuclear scientist noted that the coefficient of correlation between the amount of the substance remaining at time {eq}x {/eq} and time {eq}x {/eq} is r = -0.005. Choose from among the following the statements that is/are always true based on this computed value of r.

    I. The strength of the linear correlation between the amount of substance remaining and time is extremely strong.

    II. The strength of the linear correlation between these two variables is negligible.

    III. The strength of the association between these two variables is neither negative nor positive.

    Answers:

    • II only

    • I, II, and III

    • II and III only

    • I and II only

  • 19.

    The coefficient of correlation between the previous year's monthly sales and this year's monthly sales of a certain company is reported as r = -0.65. The strength of this association may be described as a _____.

    Answers:

    • moderate and positive linear correlation

    • weak and negative linear correlation

    • moderate and negative linear correlation

    • weak and positive linear correlation

  • 20.

    After a patient has taken some antibiotics, the computed coefficient of linear correlation between the logarithm (base 10) of the population size of a certain pathogen at certain selected time points (in sec) and time equals r = -0.97. Based on this value for r, which of the statement/s below is/are always true?

    I. The strength of the association between the logarithm (base 10) of the number of this pathogen present at any given time and time is weak or low.

    II. The strength of the linear correlation between these two variables is weak or low.

    III. The strength of the linear association between these two variables is very strong.

    IV. The strength of the linear association between these two variables is very weak.

    Answers:

    • IV only

    • I only

    • III only

    • II only

  • 21.

    A laboratory physics student is studying the relationship between the amount of current passing through a resistor and the amount of the resistance in the resistor, when the voltage drop across the resistor is kept constant. He obtained a number of measurement pairs for these two quantities of interest, then computed the correlation coefficient between the amount of current and the amount of resistance. He obtained a value of r = -0.65. Which of the following is/are always true statements based on this computed value of r?

    I. The strength of the association between the current passing through the resistor and the resistance of the resistor is low.

    II. The strength of the linear correlation between these two variables is moderately strong.

    III. The strength of the linear association between these two variables is negative.

    IV. The strength of the linear association between these two variables is positive.

    Answers:

    • I, II, and III

    • II and III only

    • II only

    • I and III only

  • 22.

    A taxonomist looking into the association between the sepal width and sepal length of the Iris setosa flower computed a correlation coefficient of r = 0.74 from a sample. The strength of this linear correlation is _____.

    Answers:

    • strong and negative

    • weak and positive

    • strong and positive

    • weak and negative

  • 23.

    A financial analyst computed the coefficient of linear correlation between a company's monthly sales during the first five years of the last decade with those of the last five years of the said decade and obtained r = 0.81. Which of the following gives the best description of the strength of this linear association?

    Answers:

    • weak and positive linear correlation

    • strong and positive linear correlation

    • weak and negative linear correlation

    • strong and negative linear correlation

  • 24.

    In a certain chemical plant that produces nitric acid from ammonia, the coefficient of linear correlation between an index of the concentration of the circulating acid produced and an index of the amount of ammonia that is wasted is reported as r = 0.40. Which of the following best describes this linear association?

    Answers:

    • extremely weak and positive

    • weak and positive

    • extremely weak and negative

    • weak and negative

  • 25.

    For the purpose of evaluating the water quality at a certain location, a researcher gathered data to relate the biochemical oxygen demand (BOD) and the time of day. The estimate of the coefficient of correlation between these two variables based on the data is r = 0.80. Which of the following best describes the association?

    Answers:

    • weak and negative linear correlation

    • weak and positive linear correlation

    • strong and positive linear correlation

    • strong and negative linear correlation

  • 26.

    A data analyst computed the coefficient of linear correlation between a company's first-quarter sales in the years 1961-1970 to its first-quarter sales 30 years later, i.e., from 1991-2000, and obtained r = 0.20. Which of the following best describes the strength of this association?

    Answers:

    • moderate and negative linear correlation

    • moderate and positive linear correlation

    • negligible and negative linear correlation

    • negligible and positive linear correlation

  • 27.

    A molecular biologist studying the growth rate of a certain species of virus computed the correlation coefficient between the number of viruses present inside a particular cell at different time points and the time. The value she obtained is r = 0.015. Based on this value for r, which of the statement/s below is/are always true?

    I. The strength of the linear correlation between the number of virus present in a cell at any given time and time is extremely strong.

    II. The strength of the linear correlation between these two variables is negligible.

    III. The strength of the linear association between these two variables is positive.

    Answers:

    • II and III only

    • I and II only

    • I, II, and III

    • II only

  • 28.

    A biochemist noted that if a certain plant species from Quebec were chilled overnight, then the coefficient of linear correlation between the ambient carbon dioxide concentration (in mL/L) and rate of carbon dioxide uptake (in μmol/m²/s) is equal to 0.74. This association between the two variables of interest is a _____.

    Answers:

    • strong and positive linear correlation

    • weak and positive linear correlation

    • weak and negative linear correlation

    • strong and negative linear correlation

  • 29.

    A recent study reported a correlation coefficient of r = 0.75 between percent body fat (%BF) and body mass index (BMI). Find the best description of this association from among the given choices.

    Answers:

    • weak and negative linear correlation

    • weak and positive linear correlation

    • strong and positive linear correlation

    • strong and negative linear correlation

  • 30.

    A zoologist looking into the relationship of time of day and body temperature among beavers computed a correlation coefficient of r = 0.37 from a dataset that he gathered. Describe the strength of the linear correlation between these two variables based on this dataset.

    Answers:

    • weak and negative

    • weak and positive

    • extremely strong and positive

    • extremely strong and negative

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