Pertemuan 21 dan 22 Analisis Regresi dan Korelasi Sederhana

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1 Pertemuan 21 dan 22 Analisis Regresi dan Korelasi Sederhana
Matakuliah : I Statistika Tahun : 2008 Versi : Revisi Pertemuan 21 dan 22 Analisis Regresi dan Korelasi Sederhana

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menghitung dugaan parameter regresi sederhana, korelasi dan menguji keberartiannya.

3 Estimasi koefisien regresi Inferensia parameter regresi
Outline Materi Estimasi koefisien regresi Inferensia parameter regresi Koefisien korelasi Koefisien determinasi Inferesia koefisien korelasi

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:

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.

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:

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.

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.

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

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.

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

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

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.

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.

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.

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.

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 ^

18 Residual for Observation i yi – yi
Residual Analysis Residual for Observation i yi – yi Standardized Residual for Observation i where: ^ ^ ^ ^

19 Contoh Soal: Reed Auto Sales
Residuals

20 Contoh Soal: Reed Auto Sales
Residual Plot

21 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 = r2

22 Uji Korelasi Sederhana
Hipotesis: Ho : r = 0 (tidak ada hubungan x dan y) Ha : r > 0, r < 0, atau r  0 Statistik uji:

23 Selamat Belajar Semoga Sukses.