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Section F
Optional: Some FYIs about SLR
Standard Error of Slopes

Just FYI: standard error of estimated slope is a combination of
variation in y-values around the regression line and the spread of
x-values
-  Definition: standard deviation of regression, called “root mean
squared error,” is a functionally average distance of any single
point from estimated mean of all y-values with the same x (i.e.,
corresponding value on regression line)
-  For simple linear regression, d.f.= n-2 and
-
Estimated standard error of slope estimate
3
Standard Error of Slopes

Estimated standard error of slope estimate

Notice this will be larger . . .
-  The more variable the y-values are around their corresponding
mean estimates on the regression line (ie: the greater sy|x is)
-  The less variable the x-values are around the mean of x:
hmm . . .
4
Actually Computation of R2

How do we actually compute R2?
-  Recall interpretation: percent of variability in y explained by x

Total variability in y?
-  Actually, for the R2 computation
5
Example: Arm Circumference and Height

“Visualization” on the scatterplot: the distance of each point from
the flat line at
squared and added together
6
R2: Arm Circumference and Height

Regression of arm circumference on height in centimeters: total
variability in y
7
Actually Computation of R2

Total variability in y not explained by x?
-  For the R2 computation
8
Example: Arm Circumference and Height

Each distance is
: this is computed for each
data point in the sample (squared and summed)
9
R2: Arm Circumference and Height

Regression of arm circumference on height in centimeters: total
variability in y not explained by x
10
Actually Computation of R2

Percentage of variability in y NOT explained by x

R2 is the percentage of variability in y explained by x
11