2. INFERENSIA KORELASI DAN REGRESI LINIER SEDERHANA Pertemuan 12
Matakuliah : I STATISTIK PROBABILITAS
Tahun : 2009
INFERENSIA KORELASI DAN REGRESI LINIER SEDERHANA Pertemuan 12

3. Materi Pengujian koefisien korelasi
Pengujian parameter regresi linier sederhana
Koefisien determinasi dan peramalan
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4. Persamaan Regresi
Persamaan matematika yang memungkinkan kita meramalkan nilai-nilai peubah tak bebas dari nilai-nilai satu atau lebih peubah bebas disebut Persamaan Regresi
Persamaan Regresi Sederhana:
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5. Testing for Significance
To test for a significant regression relationship, we must conduct a hypothesis test to determine whether the value of b1 is zero.
Two tests are commonly used
t Test
F Test
Both tests require an estimate of s 2, the variance of e in the regression model.
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6. Testing for Significance
An Estimate of s 2
The mean square error (MSE) provides the estimate
of s 2, and the notation s2 is also used.
s2 = MSE = SSE/(n-2)
where:
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7. Testing for Significance
An Estimate of s
To estimate s we take the square root of s 2.
The resulting s is called the standard error of the estimate.
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8. Testing for Significance: t Test
Hypotheses
H0: 1 = 0
Ha: 1 = 0
Test Statistic
Rejection Rule
Reject H0 if t < -tor t > t
where t is based on a t distribution with
n - 2 degrees of freedom.
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9. Contoh Soal: Reed Auto Sales
t Test
Hypotheses H0: 1 = 0
Ha: 1 = 0
Rejection Rule
For  = .05 and d.f. = 3, t.025 = 3.182
Reject H0 if t > 3.182
Test Statistics
t = 5/1.08 = 4.63
Conclusions
Reject H0
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10. Confidence Interval for 1
We can use a 95% confidence interval for 1 to test the hypotheses just used in the t test.
H0 is rejected if the hypothesized value of 1 is not included in the confidence interval for 1.
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11. Confidence Interval for 1
The form of a confidence interval for 1 is:
where b1 is the point estimate
is the margin of error
is the t value providing an area
of a/2 in the upper tail of a
t distribution with n - 2 degrees
of freedom
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12. Contoh Soal: Reed Auto Sales
Rejection Rule
Reject H0 if 0 is not included in the confidence interval for 1.
95% Confidence Interval for 1
= (1.08) =
/ or to 8.44/
Conclusion
Reject H0
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13. Testing for Significance: F Test
Hypotheses
H0: 1 = 0
Ha: 1 = 0
Test Statistic
F = MSR/MSE
Rejection Rule
Reject H0 if F > F
where F is based on an F distribution with 1 d.f. in
the numerator and n - 2 d.f. in the denominator.
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14. Example: Reed Auto Sales
F Test
Hypotheses H0: 1 = 0
Ha: 1 = 0
Rejection Rule
For  = .05 and d.f. = 1, 3: F.05 = 10.13
Reject H0 if F >
Test Statistic
F = MSR/MSE = 100/4.667 = 21.43
Conclusion
We can reject H0.
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15. Some Cautions about the Interpretation of Significance Tests
Rejecting H0: b1 = 0 and concluding that the relationship between x and y is significant does not enable us to conclude that a cause-and-effect relationship is present between x and y.
Just because we are able to reject H0: b1 = 0 and demonstrate statistical significance does not enable us to conclude that there is a linear relationship between x and y.
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16. Using the Estimated Regression Equation for Estimation and Prediction
Confidence Interval Estimate of E(yp)
Prediction Interval Estimate of yp
yp + t/2 sind
where the confidence coefficient is 1 -  and
t/2 is based on a t distribution with n - 2 d.f.
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17. Contoh Soal: Reed Auto Sales
Point Estimation
If 3 TV ads are run prior to a sale, we expect the mean number of cars sold to be:
y = (3) = 25 cars
Confidence Interval for E(yp)
95% confidence interval estimate of the mean number of cars sold when 3 TV ads are run is:
= to cars
Prediction Interval for yp
95% prediction interval estimate of the number of cars sold in one particular week when 3 TV ads are run is: = to cars ^
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