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# Statistika Dasar (11 - 12) analisis-regresi_dan_korelasi_sederhana

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## Statistika Dasar (11 - 12) analisis-regresi_dan_korelasi_sederhanaPresentation Transcript

• Pertemuan 11 - 12 ANALISIS REGRESI DAN KORELASI SEDERHANA Hdi Nasbey, M.Si Jurusan Fisika Fakultas Matematika dan Ilmu Pemgetahuan Alam
• Outline Materi
• Estimasi koefisien regresi
• Inferensia parameter regresi
• Koefisien korelasi
• Koefisien determinasi
• Inferesia koefisien korelasi
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• 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:
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Testing for Significance
• To test for a significant regression relationship, we must conduct a hypothesis test to determine whether the value of  1 is zero.
• Two tests are commonly used
• t Test
• F Test
• Both tests require an estimate of   2 , the variance of  in the regression model.
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Testing for Significance
• An Estimate of  2
• The mean square error (MSE) provides the estimate
• of  2 , and the notation s 2 is also used.
• s 2 = MSE = SSE/(n-2)
• where:
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Testing for Significance
• An Estimate of 
• To estimate  we take the square root of  2 .
• The resulting s is called the standard error of the estimate .
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Testing for Significance: t Test
• Hypotheses
• H 0 :  1 = 0
• H a :  1 = 0
• Test Statistic
• Rejection Rule
• Reject H 0 if t < - t   or t > t  
• where t   is based on a t distribution with
• n - 2 degrees of freedom.
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Contoh Soal: Reed Auto Sales
• t Test
• Hypotheses H 0 :  1 = 0
• H a :  1 = 0
• Rejection Rule
• For  = .05 and d.f. = 3, t .025 = 3.182
• Reject H 0 if t > 3.182
• Test Statistics
• t = 5/1.08 = 4.63
• Conclusions
• Reject H 0
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Confidence Interval for  1
• We can use a 95% confidence interval for  1 to test the hypotheses just used in the t test.
• H 0 is rejected if the hypothesized value of  1 is not included in the confidence interval for  1 .
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Confidence Interval for  1
• The form of a confidence interval for  1 is:
• where b 1 is the point estimate
• is the margin of error
• is the t value providing an area
• of  /2 in the upper tail of a
• t distribution with n - 2 degrees
• of freedom
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Contoh Soal: Reed Auto Sales
• Rejection Rule
• Reject H 0 if 0 is not included in the confidence interval for  1 .
• 95% Confidence Interval for  1
• = 5 +- 3.182(1.08) = 5 +- 3.44
• or 1.56 to 8.44/
• Conclusion
• Reject H 0
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Testing for Significance: F Test
• Hypotheses
• H 0 :  1 = 0
• H a :  1 = 0
• Test Statistic
• F = MSR/MSE
• Rejection Rule
• Reject H 0 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.
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• F Test
• Hypotheses H 0 :  1 = 0
• H a :  1 = 0
• Rejection Rule
• For  = .05 and d.f. = 1, 3: F .05 = 10.13
• Reject H 0 if F > 10.13.
• Test Statistic
• F = MSR/MSE = 100/4.667 = 21.43
• Conclusion
• We can reject H 0 .
Example: Reed Auto Sales 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Some Cautions about the Interpretation of Significance Tests
• Rejecting H 0 :  1 = 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 H 0 :  1 = 0 and demonstrate statistical significance does not enable us to conclude that there is a linear relationship between x and y .
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Confidence Interval Estimate of E ( y p )
• Prediction Interval Estimate of y p
• y p + t  /2 s ind
• where the confidence coefficient is 1 -  and
• t  /2 is based on a t distribution with n - 2 d.f.
Using the Estimated Regression Equation for Estimation and Prediction 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• 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 = 10 + 5(3) = 25 cars
• Confidence Interval for E ( y p )
• 95% confidence interval estimate of the mean number of cars sold when 3 TV ads are run is:
• 25 + 4.61 = 20.39 to 29.61 cars
• Prediction Interval for y p
• 95% prediction interval estimate of the number of cars sold in one particular week when 3 TV ads are run is: 25 + 8.28 = 16.72 to 33.28 cars
^ 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Residual Analysis
• Residual for Observation i
• y i – y i
• Standardized Residual for Observation i
• where:
^ ^ ^ 01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | ^
• Contoh Soal: Reed Auto Sales
• Residuals
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Contoh Soal: Reed Auto Sales
• Residual Plot
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Korelasi Linear
• Koefisien korelasi linear didefiisikan sebagai ukuran hubungan linear antara dua peubah X dan Y, dan dilambangkan dengan r.
• Ukuran hubungan linear antara dua peubah X dan Y diduga dengan koefisien korelasi contoh r yaitu
• Koefisien determinasi = r 2
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Uji Korelasi Sederhana
• Hipotesis:
• Ho :  tidak ada hubungan x dan y)
• Ha :  atau   
• Statistik uji:
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• Selamat Belajar Semoga Sukses.
01/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |