Chapter 11b

1
Chapter 11b
2
The Sampling Distributions Application

• We apply sampling theory to analyze the
  and that we calculate from the data we
  have
• The means of these sampling distributions are ß0
  and ß1 , these means are unknown
• The standard errors s(ß0) and s(ß1) are unknown,
  but they depend on the unknown value su and on
  the known X values
• SER serves as an estimate of su
• We can find standard errors of the estimators

3
The Sampling Distributions Application

• EARNSi ß0 ß1 EDi ui
• Estimated model
• EARNSi -1.315 0.79 EDi
• (1.540) (0.128)
• R20.285 SER4.361
• Info about ß1 is given on Figure 11.4 page 241

4
Interval Estimation

• Unknown regression coefficient is a point
  estimate
• Sampling theory states that every estimate is
  accompanied by some estimation error
• Interval estimate is a range of values that is
  likely to include the true value of the unknown
  coefficient
• Interval is known as a confidence interval
• The probability amount a, 1-a is known as the
  level of confidence

5
Interval Estimation

• For a two-tailed probability problem on Figure
  11.5
• a/2 Pr ( h) Pr (Z
  ),
• where h/s( )
• Pr(Z h/s( ))
• Pr (Z Zc) a/2
• h Zc s( )
• Unshaded area in the figure
• Pr ( ßj h ßj h ) 1-a

6
Interval Estimation

• h, where h Zc s( )
• h, where h tc s( ), where tc is
  determined from Pr (t tc) a/2
• Example.