Linear Correlation & Regression

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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