{"id":103,"date":"2021-01-12T22:19:50","date_gmt":"2021-01-12T22:19:50","guid":{"rendered":"https:\/\/textbooks.jaykesler.net\/introstats\/part\/linear-regression-and-correlation\/"},"modified":"2023-04-19T20:20:57","modified_gmt":"2023-04-19T20:20:57","slug":"linear-regression-and-correlation","status":"publish","type":"part","link":"https:\/\/textbooks.jaykesler.net\/introstats\/part\/linear-regression-and-correlation\/","title":{"rendered":"Linear Regression and Correlation"},"content":{"raw":"\r\n[latexpage]\r\n<\/span>\r\n
\r\n
\r\n\r\n
\r\n\"This\r\n<\/span><\/figure>\r\n
Figure <\/span>12.1<\/span> Linear regression and correlation can help you determine if an auto mechanic\u2019s salary is related to his work experience. (credit: Joshua Rothhaas)<\/span><\/div>\r\n<\/div>\r\n
\r\n

Chapter Objectives<\/span><\/h3>\r\n<\/header>
\r\n
\r\n

By the end of this chapter, the student should be able to:<\/p>\r\n\r\n

    \r\n \t
  • Discuss basic ideas of linear regression and correlation.<\/li>\r\n \t
  • Create and interpret a line of best fit.<\/li>\r\n \t
  • Calculate and interpret the correlation coefficient.<\/li>\r\n \t
  • Calculate and interpret outliers.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section><\/div>\r\n

    Professionals often want to know how two or more numeric variables are related. For example, is there a relationship between the grade on the second math exam a student takes and the grade on the final exam? If there is a relationship, what is the relationship and how strong is it?<\/p>\r\n

    In another example, your income may be determined by your education, your profession, your years of experience, and your ability. The amount you pay a repair person for labor is often determined by an initial amount plus an hourly fee.<\/p>\r\n

    The type of data described in the examples is bivariate<\/span> data \u2014 \"bi\" for two variables. In reality, statisticians use multivariate<\/span> data, meaning many variables.<\/p>\r\n

    In this chapter, you will be studying the simplest form of regression, \"linear regression\" with one independent variable (x<\/em>). This involves data that fits a line in two dimensions. You will also study correlation which measures how strong the relationship is.<\/p>\r\n\r\n<\/div>","rendered":"


    \n[latexpage]
    \n<\/span><\/p>\n

    \n
    \n

    \n\"This
    \n<\/span><\/figure>\n
    Figure <\/span>12.1<\/span> Linear regression and correlation can help you determine if an auto mechanic\u2019s salary is related to his work experience. (credit: Joshua Rothhaas)<\/span><\/div>\n<\/div>\n
    \n
    \n

    Chapter Objectives<\/span><\/h3>\n<\/header>\n
    \n
    \n

    By the end of this chapter, the student should be able to:<\/p>\n

      \n
    • Discuss basic ideas of linear regression and correlation.<\/li>\n
    • Create and interpret a line of best fit.<\/li>\n
    • Calculate and interpret the correlation coefficient.<\/li>\n
    • Calculate and interpret outliers.<\/li>\n<\/ul>\n<\/div>\n<\/section>\n<\/div>\n

      Professionals often want to know how two or more numeric variables are related. For example, is there a relationship between the grade on the second math exam a student takes and the grade on the final exam? If there is a relationship, what is the relationship and how strong is it?<\/p>\n

      In another example, your income may be determined by your education, your profession, your years of experience, and your ability. The amount you pay a repair person for labor is often determined by an initial amount plus an hourly fee.<\/p>\n

      The type of data described in the examples is bivariate<\/span> data \u2014 “bi” for two variables. In reality, statisticians use multivariate<\/span> data, meaning many variables.<\/p>\n

      In this chapter, you will be studying the simplest form of regression, “linear regression” with one independent variable (x<\/em>). This involves data that fits a line in two dimensions. You will also study correlation which measures how strong the relationship is.<\/p>\n<\/div>\n","protected":false},"parent":0,"menu_order":12,"template":"","meta":{"pb_part_invisible":false},"contributor":[],"license":[],"class_list":["post-103","part","type-part","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/parts\/103","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/parts"}],"about":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/wp\/v2\/types\/part"}],"version-history":[{"count":3,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/parts\/103\/revisions"}],"predecessor-version":[{"id":577,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/parts\/103\/revisions\/577"}],"wp:attachment":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/wp\/v2\/media?parent=103"}],"wp:term":[{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/wp\/v2\/contributor?post=103"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/wp\/v2\/license?post=103"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}