Question

Math

Posted 4 months ago

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Zhang Lei creates and sells wreaths. On her website, she gives the diameter, in inches, and weight, in pounds, of each wreath. An approximate least-squares regression line was used to predict the weight from a given diameter.
Interpret the residual for the wreath indicated in the scatterplot above.
Choose 1 answer:
(A) This wreath weighs 2 more pounds than predicted based on the diameter.
(B) This wreath weighs 2 fewer pounds than predicted based on the diameter.
(c) This wreath has a diameter 2 inches greater than predicted based on the weight.
(D) This wreath has a diameter 2 inches less than predicted based on the weight.
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Answer from Sia

Posted 4 months ago

Solution by Steps

step 2

A residual is the difference between the observed value and the value predicted by the regression line. It can be calculated as: $residual = observed\ value - predicted\ value$

step 3

The regression line provided by the asksia-ll calculator is $y = 13.6571x + 90.2$, where $y$ is the weight in pounds and $x$ is the diameter in inches

step 4

If the green arrow points to a specific data point above the trend line, it means the actual weight of the wreath is more than the weight predicted by the regression line

step 5

The residual value being positive indicates that the observed weight is greater than the predicted weight by the amount of the residual. If the residual is 2 pounds, it means the wreath weighs 2 more pounds than predicted

A

Key Concept

Residual in Linear Regression

Explanation

A residual is the difference between the observed value and the predicted value from the regression line. A positive residual indicates the observed value is greater than the predicted value.

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