2453 Correlation & Causality

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2453 Correlation & Causality - Quiz

The Coefficient of Determination is generally measured as a percentage. If it is 95% then the statement would read as :
95% of the variation of the dependent variable (y variable), can be explained by the variation in the independent variable (x variable)

Questions and Answers
  • 1. 
    Jack is on a fitness campaign.He is measuring his improvement by counting the number of pushups he can do in one minute.He measures his progress at the end of each week.According to the line of linear regression, he has a Correlation Coefficient of 0.94.Which statement is most correct : - ProProfs

    Jack is on a fitness campaign.He is measuring his improvement by counting the number of pushups he can do in one minute.He measures his progress at the end of each week.According to the line of linear regression, he has a Correlation Coefficient of 0.94.Which statement is most correct :

    • A.

      94% of the variation in his push up count can be explained by the number of weeks he has attended training

    • B.

      94% of the variation in his weekly attendance explained by the variation in his push-up count

    • C.

      89% of the variation in his push up count can be explained by the number of weeks he has attended training

    • D.

      89% of the variation in his weekly attendance explained by the variation in his push-up count

    • E.

      There relationship between attendance and pushups is non-linear

    Correct Answer
    C. 89% of the variation in his push up count can be explained by the number of weeks he has attended training
    Explanation
    The correlation coefficient of 0.94 indicates a strong positive linear relationship between the number of weeks Jack has attended training and his push up count. However, the statement "94% of the variation in his push up count can be explained by the number of weeks he has attended training" is not correct. The correct statement is "89% of the variation in his push up count can be explained by the number of weeks he has attended training." This means that the number of weeks attended training explains 89% of the variability in Jack's push up count.

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  • 2. 
    Paddy is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week. According to the line of linear regression, he has a Correlation Coefficient of 0.91 Which statement is most correct : - ProProfs

    Paddy is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week. According to the line of linear regression, he has a Correlation Coefficient of 0.91 Which statement is most correct :

    • A.

      91% of the variation in his push up count can be explained by the number of weeks he has attended training

    • B.

      91% of the variation in his weekly attendance explained by the variation in his push-up count

    • C.

      82% of the variation in his push up count can be explained by the number of weeks he has attended training

    • D.

      82% of the variation in his weekly attendance explained by the variation in his push-up count

    • E.

      The relationship between attendance at training and pushups is non-linear

    Correct Answer
    E. The relationship between attendance at training and pushups is non-linear
  • 3. 
    Jack is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week. According to the line of linear regression, he has an 'r' value of 0.94. Which statement is most correct : - ProProfs

    Jack is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week. According to the line of linear regression, he has an 'r' value of 0.94. Which statement is most correct :

    • A.

      94% of the variation in his push up count can be explained by the number of weeks he has attended training

    • B.

      94% of the variation in his weekly attendance explained by the variation in his push-up count

    • C.

      89% of the variation in his push up count can be explained by the number of weeks he has attended training

    • D.

      89% of the variation in his weekly attendance explained by the variation in his push-up count

    • E.

      There relationship between attendance and pushups is non-linear

    Correct Answer
    C. 89% of the variation in his push up count can be explained by the number of weeks he has attended training
    Explanation
    The correct answer is "89% of the variation in his push up count can be explained by the number of weeks he has attended training." This means that 89% of the changes or differences in Jack's push up count can be attributed to the number of weeks he has attended training. The remaining 11% of the variation may be due to other factors that are not accounted for in this analysis.

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  • 4. 
    Jack is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week. According to the line of linear regression, he has Coefficient of Determintion of 0.89. Which statement is most correct : - ProProfs

    Jack is on a fitness campaign. He is measuring his improvement by counting the number of pushups he can do in one minute. He measures his progress at the end of each week. According to the line of linear regression, he has Coefficient of Determintion of 0.89. Which statement is most correct :

    • A.

      94% of the variation in his push up count can be explained by the number of weeks he has attended training

    • B.

      94% of the variation in his weekly attendance explained by the variation in his push-up count

    • C.

      89% of the variation in his push up count can be explained by the number of weeks he has attended training

    • D.

      89% of the variation in his weekly attendance explained by the variation in his push-up count

    • E.

      There relationship between attendance and pushups is non-linear

    Correct Answer
    C. 89% of the variation in his push up count can be explained by the number of weeks he has attended training
    Explanation
    The correct answer is "89% of the variation in his push up count can be explained by the number of weeks he has attended training". This means that the number of weeks Jack has attended training can account for 89% of the changes in his push up count. The coefficient of determination, also known as R-squared, measures the proportion of the dependent variable's variance that can be explained by the independent variable(s). In this case, the independent variable is the number of weeks attended training and the dependent variable is the push up count.

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  • 5.