Question

Math

Posted 4 months ago

```
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 $y$.
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

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.

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