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regression/correlation coefficient which value of r represents data wit…

Question

regression/correlation coefficient
which value of r represents data with a strong negative linear correlation between two variables?

  1. -1.07
  2. -0.89
  3. -0.14
  4. 0.92

which value of r represents data with a strong positive linear correlation between two variables?

  1. 0.89
  2. 0.34
  3. 1.04
  4. 0.01

6 the points in the scatter plot below represent the ages of automobiles and their values. based on this scatter plot, it would be reasonable to conclude:

  1. age and value have a coefficient of correlation that is less than zero.
  2. age and value have a coefficient of correlation that is equal to zero.
  3. age and value have a coefficient of correlation that is between zero and 0.5.
  4. age and value have a coefficient of correlation that is greater than 0.5.

a study compared the number of years of education a person received and that persons average yearly salary. it was determined that the relationship between these two quantities was linear and the correlation coefficient was 0.91. which conclusion can be made based on the findings of this study?

  1. there was a weak relationship.
  2. there was a strong relationship.
  3. there was no relationship.
  4. there was an unpredictable relationship.

what is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth?
3 as shown in the table below, a persons target heart rate during exercise changes as the person gets older.

age (years)target heart rate (beats per minute)
25132
30129
35125
40122
45119
50115

which value represents the linear correlation coefficient, rounded to the nearest thousandth, between a persons age, in years, and that persons target heart rate, in beats per minute?

  1. -0.999
  2. -0.664
  3. 0.998
  4. 1.503

day 5 ~ wednesday

Explanation:

Question 1: Which value of $r$ represents data with a strong negative linear correlation between two variables?
  1. Recall the range of the correlation - coefficient $r$: The correlation coefficient $r$ ranges from - 1 to 1, i.e., $-1\leq r\leq1$. A value of $r$ close to - 1 indicates a strong negative linear correlation.
  • Option 1: $r=-1.07$ is outside the range of the correlation coefficient, so it is not valid.
  • Option 2: $r = - 0.89$ is close to - 1 and is within the range $[-1,1]$.
  • Option 3: $r=-0.14$ is a weak negative correlation as it is far from - 1.
  • Option 4: $r = 0.92$ is a strong positive correlation.
  1. Conclusion: The value of $r$ that represents a strong negative linear correlation is $r=-0.89$.
Question 2: Which value of $r$ represents data with a strong positive linear correlation between two variables?
  1. Recall the properties of the correlation - coefficient: A value of $r$ close to 1 indicates a strong positive linear correlation.
  • Option 1: $r = 0.89$ is close to 1 and within the range $[-1,1]$.
  • Option 2: $r = 0.34$ is a weak positive correlation as it is far from 1.
  • Option 3: $r = 1.04$ is outside the range of the correlation coefficient, so it is not valid.
  • Option 4: $r = 0.01$ is a very weak positive correlation.
  1. Conclusion: The value of $r$ that represents a strong positive linear correlation is $r = 0.89$.
Question 3: The points in the scatter - plot represent the ages of automobiles and their values. Based on this scatter - plot, it would be reasonable to conclude:
  1. Analyze the relationship between age and value of automobiles: Generally, as the age of an automobile increases, its value decreases. This indicates a negative correlation.
  • Option 1: Age and value have a coefficient of correlation that is less than zero. This is correct because of the negative relationship (older cars tend to be worth less).
  • Option 2: A correlation coefficient of zero means no linear relationship, but there is a negative linear trend here, so this is incorrect.
  • Option 3: A correlation coefficient between 0 and 0.5 would indicate a weak positive correlation, which is not the case here.
  • Option 4: A correlation coefficient greater than 0.5 would indicate a strong positive correlation, which is not the case here.
  1. Conclusion: Age and value have a coefficient of correlation that is less than zero.
Question 4: A study compared the number of years of education a person received and that person's average yearly salary. It was determined that the relationship between these two quantities was linear and the correlation coefficient was 0.91. Which conclusion can be made based on the findings of this study?
  1. Recall the interpretation of the correlation coefficient: A correlation coefficient close to 1 (in this case, $r = 0.91$) indicates a strong positive linear relationship.
  • Option 1: A weak relationship would be indicated by a value of $r$ close to 0.
  • Option 2: Since $r = 0.91$ is close to 1, there was a strong relationship.
  • Option 3: A correlation coefficient of 0 would indicate no relationship.
  • Option 4: An unpredictable relationship would not have a high - magnitude correlation coefficient.
  1. Conclusion: There was a strong relationship.
Question 5: As shown in the table, a person's target heart rate during exercise changes as the person gets older. Which value represents the linear correlation coefficient, rounded to the nearest thousandth, between a person's age, in years, and that person's target heart rate, i…

Answer:

  1. 2) $-0.89$
  2. 1) $0.89$
  3. 1) Age and value have a coefficient of correlation that is less than zero.
  4. 2) There was a strong relationship.
  5. 1) $-0.999$