Math  /  Data & Statistics

QuestionFor each residual plot below, determine whether a linear model is appropriate, and if not, why not.
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Studdy Solution

STEP 1

What is this asking? Which of these plots show that a straight line isn't the best fit for the data? Watch out! Random scatter is *good* in a residual plot!
It means the line is a good fit.

STEP 2

1. Check Plot 1
2. Check Plot 2
3. Check Plot 3

STEP 3

Look at Plot 1!
The residuals make a *curve*.
That's a *big* sign that a linear model *isn't* appropriate.
It means the relationship between "Time" and whatever we're measuring is probably curved, not straight.

STEP 4

Plot 2 is a *party* of randomness!
The residuals are scattered all over the place with no obvious pattern.
This is *exactly* what we want to see if a linear model is a good fit.
The randomness tells us the line is doing a good job capturing the relationship between "X" and whatever we're measuring.

STEP 5

Plot 3 shows a *fanning out* pattern.
The residuals get bigger as "X" increases.
This means our predictions are getting *less accurate* as "X" gets bigger.
A linear model might *not* be the best choice here.
It suggests that the relationship between "X" and what we're measuring might not be consistent across all values of "X".

STEP 6

Plot 1 and Plot 3 show that a linear model is not appropriate.
Plot 1 shows a curved pattern, and Plot 3 shows a fanning-out pattern, both indicating that a linear model is not the best fit for the data.

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