INFERENSIA KORELASI DAN REGRESI LINIER SEDERHANA Pertemuan 12 Matakuliah : I0272 - STATISTIK PROBABILITAS Tahun : 2009 INFERENSIA KORELASI DAN REGRESI LINIER SEDERHANA Pertemuan 12

Materi Pengujian koefisien korelasi Pengujian parameter regresi linier sederhana Koefisien determinasi dan peramalan Bina Nusantara University

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: Bina Nusantara University

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. Bina Nusantara University 5 5

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: Bina Nusantara University 6 6

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. Bina Nusantara University 7 7

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. Bina Nusantara University 8 8

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 Bina Nusantara University 9 9

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. Bina Nusantara University 10 10

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 Bina Nusantara University 11 11

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 = 5 +- 3.182(1.08) = 5 +- 3.44 / or 1.56 to 8.44/ Conclusion Reject H0 Bina Nusantara University 12 12

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. Bina Nusantara University 13 13

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 > 10.13. Test Statistic F = MSR/MSE = 100/4.667 = 21.43 Conclusion We can reject H0. Bina Nusantara University 14 14

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. Bina Nusantara University 15 15

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. Bina Nusantara University 16 16

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(yp) 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 yp 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 ^ Bina Nusantara University 17