1.5 REGRESSION VERSUS CORRELATIONCl

1.5 REGRESSION VERSUS CORRELATION
Closely related to but conceptually very much different from regression
analysis is correlation analysis, where the primary objective is to measure
the strength or degree of linear association between two variables. The correlation
coefficient, which we shall study in detail in Chapter 3, measures
this strength of (linear) association. For example, we may be interested in
finding the correlation (cocoefficient) between smoking and lung cancer,
between scores on statistics and mathematics examinations, between high
school grades and college grades, and so on. In regression analysis, as already
noted, we are not primarily interested in such a measure. Instead, we
try to estimate or predict the average value of one variable on the basis
of the fixed values of other variables. Thus, we may want to know whether
we can predict the average score on a statistics examination by knowing a
student’s score on a mathematics examination.
Regression and correlation have some fundamental differences that are
worth mentioning. In regression analysis there is an asymmetry in the way
the dependent and explanatory variables are treated. The dependent variable
is assumed to be statistical, random, or stochastic, that is, to have a
probability distribution. The explanatory variables, on the other hand, are
assumed to have fixed values (in repeated sampling),7 which was made explicit
in the definition of regression given in Section 1.2. Thus, in Figure 1.2
we assumed that the variable age was fixed at given levels and height measurements
were obtained at these levels. In correlation analysis, on the other hand, we treat any (two) variables symmetrically; there is no distinction
between the dependent and explanatory variables. After all, the correlation
between scores on mathematics and statistics examinations is the
same as that between scores on statistics and mathematics examinations.
Moreover, both variables are assumed to be random. As we shall see, most
of the correlation theory is based on the assumption of randomness of variables,
whereas most of the regression theory to be expounded in this book is
conditional upon the assumption that the dependent variable is stochastic
but the explanatory variables are fixed or nonstochastic

Hasil (Bahasa Indonesia) 1:

1.5 REGRESI VERSUS KORELASIErat terkait tetapi konseptual sangat berbeda dari regresiAnalisis adalah analisis korelasi, dimana tujuan utama adalah untuk mengukurkekuatan atau tingkat linier Asosiasi antara dua variabel. KorelasiKoefisien, yang kita harus mengkaji secara rinci dalam bab 3, langkah-langkahkekuatan ini ikatan (linier). Sebagai contoh, kita mungkin akan tertarikmenemukan korelasi (cocoefficient) antara merokok dan kanker paru-paru,antara nilai ujian Statistik dan matematika, antara tinggitingkatan sekolah dan perguruan tinggi nilai, dan sebagainya. Dalam analisis regresi, sebagaimana telahmencatat, kami tidak terutama tertarik pada ukuran seperti. Sebaliknya, kitamencoba untuk memperkirakan atau memperkirakan nilai rata-rata satu variabel atas dasarnilai-nilai tetap variabel-variabel lainnya. Dengan demikian, kita mungkin ingin tahu apakahkita bisa memprediksi Skor rata-rata pada pemeriksaan Statistik dengan mengetahuisiswa Skor pada pemeriksaan matematika.Regresi dan korelasi memiliki beberapa perbedaan mendasar yanglayak disebut. Dalam analisis regresi ada asimetri di jalankepelangganan dan penjelasan variabel diperlakukan. Variabel dependendiasumsikan tidak statistik, acak, atau stokastik, yang memilikiProbabilitas Distribusi. Variabel penjelasan, di sisi lain, adalahdiasumsikan tetap nilai (dalam berulang sampling), 7 yang dibuat eksplisitdalam definisi regresi yang diberikan dalam bagian 1.2. Dengan demikian, pada gambar 1.2kita mengasumsikan bahwa usia variabel ditetapkan pada tingkat dan ketinggian pengukuranDiperoleh pada tingkat ini. Dalam analisa korelasi, di sisi lain, kami memperlakukan setiap variabel (dua) simetris; ada tidak ada perbedaanantara variabel-variabel kepelangganan dan penjelasan. Setelah semua, korelasidi antara nilai ujian matematika dan Statistiksama seperti antara nilai ujian Statistik dan matematika.Selain itu, kedua variabel diasumsikan acak. Seperti yang akan kita lihat, palingkorelasi teori didasarkan pada asumsi keacakan variabel,sedangkan sebagian besar teori regresi diuraikan dalam buku inibersyarat berdasarkan asumsi bahwa variabel dependen stokastiktapi jelas variabel tetap atau nonstochastic