Ch 12.1 and 12.2
Inference for Linear Regression and Transforming to
Achieve Linearity
We remember best fit lines: y =ax + b or y = a + bx
Now we are going to construct a confidence interval for the slope of the regression line.
EQUATION (from ch 8.1): Stat ± critical value(standard deviation of stat)
Margin of error
Since we don’t have the standard deviation of the slope, we use
the standard error or SE instead
b ± t*SEb
with df = n - 2
Remember to find t* on a graphing calc (TI-84 or above): invT(% above, df)
…so for a 95% CI, the % above = 2.5% or .025
-----------------------------------------------------------------------------------------------------Now we are going to determine if Ho: There is no evidence of a linear relationship
or
Ha: There is evidence of a linear relationship
HOW?
We focus on the slope of the line (β), with Ho: β = 0
and
Ha: β ≠ 0 (there is a relationship)
β > 0 (positive relationship)
β < 0 (negative relationship)
We use a modified t-test for this…either with the equation
with df = n – 2
 On a graphing calc: STAT  TEST, E: LinRegTTest. The x-values must be
in L1 and the y-values must be in L2. This will give you the p-value, as well as
the equation, correlation coefficient, and r2 values for the line.
Don’t forget…
In addition, all conditions must be met…
linear: the relationship should be linear (check residual)
independent: individual observations are independent
normal: the y-values have a normal distribution (the graph is not skewed)
equal variance: σ of y is roughly the same for all x (look at the residual and make sure
the distance of the points from the x-axis doesn’t change as x gets bigger or
smaller
random: the data points come from a randomized survey or experiment
To help remember them, think LINER
L
I
N
E
R
If you need it…
SEb =
where s is the standard deviation of the residual