Display of output

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Lesson 29b
Regression Via Excel

• Display of output
• Interpreting components of output
• Multiple regression

Main Ideas
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• 1. Regression Output From Excel

Mothers height (x), Daughters height (y)
Output by each arrow is explained on next 3
slides
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• 2. Regression Statistics

Multiple R is the absolute value of correlation
between x and y. It is also the correlation
between observed y and predicted y
R2
RMSE is called Standard Error by Excel. This is
the wrong term for RMSE .
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• 3. ANOVA

p-value for F statistic
SSE MSE
F Regression MS/ Residual MS. It tests whether
or not the x contributes significantly to
prediction of y. It serves the same purpose as
testing for significance of the slope.
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• 4. Coefficients

Standard error and t-statistic for slope
Lower and upper limits for 95 CI for pop. slope.
Intercept Slope
Standard error , t-stat, etc. for intercept are
analogous to the corresponding quantities for
slope.
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• 5. Multiple Regression
• More than one predictor variable.
• For instance, we may wish to predict daughters
  height using both mothers height and fathers
  height.
• General form of equation for two predictor
  variables

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• 6. Analysis of Multiple Regression Data
• Principles are the same as with one predictor
  variable. However, simple equations for
  coefficients are not available.
• Rely on computer analysis for multiple
  regression.

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• 7. Quadratic Model
• A quadratic model has the general form
• This can be thought of as a multiple regression
  model with x1 x , and x2 x2

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Are all computer print-outs for regression like
Excel?
Most have similar sorts of information. If you
have another program, analyze the mothers height
- daughters height data and compare to the Excel
output.
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