The graph displays a residual plot that was constructed after running a least-squares regression on a set of bivariate numerical data $(x, y)$.

What can you conclude from this graph?

Choose 1 answer:
(A) There appears to be a linear relationship between $x$ and $y$.
(B) There does not appear to be a linear relationship between $x$ and $y$.

Question

The graph displays a residual plot that was constructed after running a least-squares regression on a set of bivariate numerical data $(x, y)$.

What can you conclude from this graph?

Choose 1 answer:
(A) There appears to be a linear relationship between $x$ and $y$.
(B) There does not appear to be a linear relationship between $x$ and $y$.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ A residual plot is used to assess the appropriateness of a linear regression model. ‖ ‖ step 2 ⋮ If the residuals are randomly scattered around the horizontal axis (y = 0), this suggests that the linear model is appropriate for the data. ‖ ‖ step 3 ⋮ The absence of patterns or systematic structures in the scatter plot of residuals indicates that there is no violation of the assumption of linearity. ‖ ‖ step 4 ⋮ Since the question states that the distribution of the points appears to be relatively random with no clear pattern, it suggests that the linear model fits the data well. ‖ ***A*** ∻Key Concept∻ ⚹Residual Plot Analysis⚹ ∻Explanation∻ ⚹A residual plot with randomly scattered residuals around the horizontal axis suggests a good fit for a linear regression model, indicating a linear relationship between the independent and dependent variables.⚹◊What is the formula for calculating the residual in a least-squares regression model?⍭ Generate me a similar question◊

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