{"id":1190,"date":"2015-08-27T10:36:12","date_gmt":"2015-08-27T09:36:12","guid":{"rendered":"http:\/\/pcool.dyndns.org:8080\/statsbook\/?page_id=1190"},"modified":"2025-06-18T08:22:05","modified_gmt":"2025-06-18T07:22:05","slug":"questions-curve-fitting","status":"publish","type":"page","link":"https:\/\/pcool.dyndns.org\/index.php\/questions-curve-fitting\/","title":{"rendered":"Questions Curve Fitting"},"content":{"rendered":"

Consider the following data set:<\/p>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t
x<\/th>y<\/th>\n<\/tr>\n<\/thead>\n
3<\/td>1.2<\/td>\n<\/tr>\n
4<\/td>1.4<\/td>\n<\/tr>\n
5<\/td>1.6<\/td>\n<\/tr>\n
6<\/td>1.75<\/td>\n<\/tr>\n
7<\/td>1.85<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

The data is also provided in Q8-1.rda <\/a>(the data frame is called Q8).<\/p>\n

    \n
  1. Plot the data, draw the regression line and estimate the equation of the line<\/li>\n
  2. What is the correlation coefficient?<\/li>\n
  3. Interpolate the y-value for x = 5.5<\/li>\n
  4. Extrapolate the y-values for x = 0.1 and x = 15<\/li>\n<\/ol>\n

    Consider the extended data set below:<\/p>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
    x<\/th>y<\/th>\n<\/tr>\n<\/thead>\n
    0.1<\/td>-1.25<\/td>\n<\/tr>\n
    0.2<\/td>-0.7<\/td>\n<\/tr>\n
    1<\/td>0.4<\/td>\n<\/tr>\n
    2<\/td>0.9<\/td>\n<\/tr>\n
    3<\/td>1.2<\/td>\n<\/tr>\n
    4<\/td>1.4<\/td>\n<\/tr>\n
    5<\/td>1.6<\/td>\n<\/tr>\n
    6<\/td>1.75<\/td>\n<\/tr>\n
    7<\/td>1.85<\/td>\n<\/tr>\n
    8<\/td>1.95<\/td>\n<\/tr>\n
    9<\/td>2.05<\/td>\n<\/tr>\n
    10<\/td>2.1<\/td>\n<\/tr>\n
    12<\/td>2.25<\/td>\n<\/tr>\n
    14<\/td>2.35<\/td>\n<\/tr>\n
    15<\/td>2.4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

    The data is also provided in Q8-2.rda<\/a> (the data frame is called Q8Extended).<\/p>\n

      \n
    1. \n
        \n
      1. Plot these data in a graph<\/li>\n
      2. What is the relation between x and y and what is the value of the correlation coefficient?<\/li>\n
      3. What are the y-values for x = 0.1 and x = 15?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

        A Study is undertaken to validate the use of an iPhone inclinometer to measure knee flexion. The \u2018Gold Standard\u2019 is a Lafayette Long-Armed Goniometer. Multiple knee flexion angles are measured with each device and the paired data are provided in the file goniometer.rda<\/a>.
        \n<\/em><\/p>\n

          \n
        1. \n
            \n
          1. Create a scatterplot with equal axes and add a line x=y.<\/li>\n
          2. Calculate the Pearson’s correlation coefficient.<\/li>\n
          3. Calculate the Interclass Correlation (ICC).<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

            Consider the following data set: The data is also provided in Q8-1.rda (the data frame is called Q8). Plot the data, draw the regression line and estimate the equation of the line What is the correlation coefficient? Interpolate the y-value for x = 5.5 Extrapolate the y-values for x = 0.1 and x = 15 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-1190","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/1190","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/comments?post=1190"}],"version-history":[{"count":6,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/1190\/revisions"}],"predecessor-version":[{"id":4096,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/1190\/revisions\/4096"}],"wp:attachment":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/media?parent=1190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}