Linear Correlation & Regression

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| By Dana Deuitch
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Dana Deuitch
Community Contributor
Quizzes Created: 3 | Total Attempts: 2,030
Questions: 14 | Attempts: 218

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Linear Correlation & Regression - Quiz

Calculate a correlation coefficient, use it to classify the correlation, then calculate the equation of the line of best fit and use that equation to make predictions.


Questions and Answers
  • 1. 

    Find 

    Explanation
    Add up the values in the x-column (number of siblings)

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  • 2. 

    Find 

    Explanation
    Add up the y-values (overall mark)

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  • 3. 

    Find 

    Explanation
    Square each of the x-values first (number of siblings) then add them up

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  • 4. 

    Find 

    Explanation
    Square each of the y-values first (overall mark) then add them up

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  • 5. 

    Find 

    Explanation
    Multiply x by y (siblings times mark) then add up the results

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  • 6. 

    Calculate the correlation coefficient. Round your answer to 2 decimal places.

    Explanation
    The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is -0.95, which indicates a strong negative linear relationship between the variables. This means that as one variable increases, the other variable tends to decrease. The negative sign indicates the direction of the relationship, and the absolute value of 0.95 indicates the strength, with values closer to 1 indicating a stronger relationship.

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  • 7. 

    Calculate the slope of the line of best fit. Round your answer to 2 decimal places.

    Explanation
    The slope of the line of best fit is equal to the given value of -8.13.

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  • 8. 

    Classify the relationship between number of siblings and overall mark.

    Explanation
    What does the correlation coefficient tell you about the relationship?
    Hint: You should have 4 terms in your classification!!

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  • 9. 

    Calculate the y-intercept of the line of best fit. Round to 2 decimal places.

    Explanation
    Remember y-bar is the mean of y, and x-bar is the mean of x.

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  • 10. 

    Write the equation of the line of best fit. Leave all values at 2 decimal places, do not use capitals and do not use spaces.

    Explanation
    y=ax+b

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  • 11. 

    What mark would you expect from a person with 6 siblings? Round to the nearest whole mark.

    Explanation
    Substitute into your equation for x=6.

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  • 12. 

    Is estimating the mark of a person with 6 siblings interpolation or extrapolation?

    • A.

      Interpolation

    • B.

      Extrapolation

    • C.

      Neither

    • D.

      Both

    Correct Answer
    B. Extrapolation
    Explanation
    Is 6 siblings between your min & max number of siblings given, or outside of this range?

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  • 13. 

    If a person who has a mark of 78, how many siblings would you expect them to have? Remember to round! A person can't have part of a sibling!

    Correct Answer
    2
    Explanation
    Based on the information given, there is no direct correlation between a person's mark of 78 and the number of siblings they would have. The answer of 2 is likely a random guess or unrelated to the question. Without further context or information, it is not possible to determine the number of siblings a person would have based solely on their mark.

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  • 14. 

    Is determining the number of siblings for a person with a mark of 78, interpolation or extrapolation?

    • A.

      Interpolation

    • B.

      Extrapolation

    • C.

      Neither

    • D.

      Both

    Correct Answer
    A. Interpolation
    Explanation
    Interpolation is the process of estimating values within a set of known data points. In this case, determining the number of siblings for a person with a mark of 78 falls within the range of known data points, so it is considered interpolation. Extrapolation, on the other hand, involves estimating values outside the range of known data points, which is not applicable in this scenario. Therefore, the correct answer is interpolation.

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