STAT E-50 - Introduction to Statistics
Inferences for Regression
The fitted regression line has the equation
ˆ
0
1
y = b +b x
.
Now we can find
confidence intervals and perform hypothesis tests for the slope.
The idealized regression line is
y
0
1
μ
=
β
+
β
x +
ε
where
ε
is the error
y -
μ
y
for
each data point (x, y).
ε
= “epsilon”
1

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Assumptions for the model and the errors:
1.
Linearity Assumption
Straight Enough Condition: does the scatterplot appear linear?
Check the residuals to see if they appear to be randomly scattered
2.
Independence Assumption:
the errors must be mutually independent
Randomization Condition:
the individuals are a random sample
Check the residuals for patterns, trends, clumping
2

3.
Equal Variance Assumption:
the variability of y should be about the
same for all values of x
Does The Plot Thicken? Condition:
Is the spread about the line nearly constant in the scatterplot?
Check the residuals for any patterns
3

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