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.

Question

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.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To interpret the residual for the wreath indicated in the scatterplot, we need to understand the concept of residuals in the context of linear regression. ‖ ‖ 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.◊What is the formula for calculating the residual in linear regression analysis?⍭ Generate me a similar question◊⚹

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