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</h1> <ol class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1065/statistics-and-probability.html">Statistics and Probability</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">4.4 Bivariate data & Linear Correlation</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <h2><img alt="" src="../../files/Stats/bvd/bvd-medium-1.jpeg" style="float: left; width: 100px; height: 100px;">Bivariate Data</h2> <p>This topic is all about looking for relationships between variables. Does life expectancy depend on GDP? By collecting 2 variables about the things we survey we can use scatter graphs to represent the data and then look for correlation and models that we can then use for prediction.</p> <hr> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p><span id="docs-internal-guid-3a96fd7d-7fff-9f9c-8bc6-f5a9f75c7254"></span></p> <p dir="ltr"><span id="docs-internal-guid-3a96fd7d-7fff-9f9c-8bc6-f5a9f75c7254">In this unit you should learn to…</span></p> <ul style="list-style-type:disc;"> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">Collect, present and analyse 2 variable data looking for linear correlation</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">Calculate the Pearson's Product Moment Correlation Coefficient as a measure of degree of correlation</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">Calculate and use a regression line that models data that shows correlation.</p> </li> </ul> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Slides Gallery</p> </div> </div> <div class="panel-body"> <div> <p>Use these slides to review the material and key points covered in the videos.</p> <div id="carousel-255" class="dynamic-gallery carousel slide" data-id="255"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-255/bvd2-nologos001.jpeg" data-fancybox="gallery-255" title="" data-caption=""><img alt="" src="../../../std-galleries/15-255/bvd2-nologos001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-255/bvd2-nologos002.jpeg" data-fancybox="gallery-255" title="" data-caption=""><img alt="" src="../../../std-galleries/15-255/bvd2-nologos002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-255/bvd2-nologos003.jpeg" data-fancybox="gallery-255" title="" data-caption=""><img alt="" src="../../../std-galleries/15-255/bvd2-nologos003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-255/bvd2-nologos004.jpeg" data-fancybox="gallery-255" title="" data-caption=""><img alt="" src="../../../std-galleries/15-255/bvd2-nologos004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-255/bvd2-nologos005.jpeg" data-fancybox="gallery-255" title="" data-caption=""><img alt="" src="../../../std-galleries/15-255/bvd2-nologos005.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-255/bvd2-nologos006.jpeg" data-fancybox="gallery-255" title="" data-caption=""><img alt="" src="../../../std-galleries/15-255/bvd2-nologos006.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-255/bvd2-nologos007.jpeg" data-fancybox="gallery-255" title="" data-caption=""><img alt="" src="../../../std-galleries/15-255/bvd2-nologos007.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-255" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-255" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-255/bvd2-nologos001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-255/bvd2-nologos002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-255/bvd2-nologos003-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-255/bvd2-nologos004-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-255/bvd2-nologos005-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-255/bvd2-nologos006-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-255/bvd2-nologos007-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>1. Bivariate data and Scatter diagrams</p> </div> </div> <div class="panel-body"> <div> <p>This video is an introduction to the concept of bivariate data and looking for relationships/correlation</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594541968"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>2. Scattergraphs</p> </div> </div> <div class="panel-body"> <div> <p>This is about plotting and interpreting these diagrams</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594542535"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>3. Correlation </p> </div> </div> <div class="panel-body"> <div> <p>This video is about judging correlation</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594547408"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>4. Product moment correlation coefficient</p> </div> </div> <div class="panel-body"> <div> <p>This is about calculating this key measurement of correlation</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594543515"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>5. Lines of best fit</p> </div> </div> <div class="panel-body"> <div> <p>This is about how lines of best fit become calculated 'Least squares regression lines' that are accurate measures of the pattern.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594544372"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>6. Making predictions</p> </div> </div> <div class="panel-body"> <div> <p>If we have correlation, and we have calculated a regression line, we can use it to make predictions.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/594545778"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <p><em><strong>Revision Card</strong></em> - Review this condensed 'key point' revision card to help you check and keep ideas fresh in your mind.</p> <p style="text-align: center;"><img alt="" src="../../files/Stats/bvd/rc1.001.jpeg" style="width: 700px; height: 525px;"></p> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test yourself</p> </div> </div> <div class="panel-body"> <div> <h4>Self Checking Quiz</h4> <p>Practice your understanding on these quiz questions. Check your answers when you are done and read the hints where you got stuck. If you find there are still some gaps in your understanding then go back to the videos and slides above.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="tib-quiz" data-stats="15-329-2266"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>Question 1</p><p>Look at the scatter diagrams below.</p><p style="text-align: center;"><img alt="" src="../../files/Stats/bvd/q1.jpg" style="width: 700px; height: 450px;"></p><p>Write the letter corresponding to the diagram next to the descriptions of the correlation</p></div><div class="q-answer"><p>Write A, B, C, D, E in the boxes below (Use them all)</p><p>Strong Positive correlation <input type="text" style="height: auto;" data-c="C"> <span class="review"></span> </p><p>Moderate positive correlation <input type="text" style="height: auto;" data-c="A"> <span class="review"></span> </p><p>No correlation <input type="text" style="height: auto;" data-c="E"> <span class="review"></span> </p><p>Moderate negative correlation <input type="text" style="height: auto;" data-c="B"> <span class="review"></span> </p><p>Strong negative correlation <input type="text" style="height: auto;" data-c="D"> <span class="review"></span> </p></div><div class="q-explanation"><p>Linear Correlation is a measure of how close the points are to a straightline. The gradient of the line is not a consideration.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>...</p><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>Question 2</p><p>Which of the following would it be possible to show on a scatter graph. Write either 'Y' or 'N' next to each.</p></div><div class="q-answer"><p>1. 100 students had the heigth and armspan measured. <input type="text" style="height: auto;" data-c="Y"> <span class="review"></span> </p><p>2. 200 Cars were surveyed for their make and engine size <input type="text" style="height: auto;" data-c="N"> <span class="review"></span> </p><p>3. 1000 trees were surveyed for their height and diameter at the base. <input type="text" style="height: auto;" data-c="Y"> <span class="review"></span> </p><p>4. 75 Countries were surveyed to compare their GDP with infant mortality <input type="text" style="height: auto;" data-c="Y"> <span class="review"></span> </p><p>5. 100 25 year olds were asked for their gender and had their 100 sprint time measured <input type="text" style="height: auto;" data-c="N"> <span class="review"></span></p></div><div class="q-explanation"><p>For a scatter diagram, you need 2 pieces of numerical data about each of the things you survey.</p><p>1. Y - Height and Armspan are both numericam</p><p>2. N - Car make is categorical</p><p>3. Y - Both numerical measures about the trees</p><p>4. Y - Both numerical measures</p><p>5. N - Gender is categorical</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>Question 3</p><p>Thee table below shows the IB scores of students who studied Geography and History</p><p style="text-align: center;"><img alt="" src="../../files/Stats/bvd/q3.jpg" style="width: 150px; height: 277px;"></p></div><div class="q-answer"><p>a) Calculate the the Pearsons product moment correlation coefficient to 3sf</p><p>r = <input type="text" style="height: auto;" data-c="0.676"> <span class="review"></span> </p><p>b) The equation of the regression line for this data is y = mx + c. What are the values of m and c, rounded to 3sf.</p><p>m = <input type="text" style="height: auto;" data-c="0.506"> <span class="review"></span> , c = <input type="text" style="height: auto;" data-c="2.25"> <span class="review"></span> </p><p>c) Using the rounded values for the regression line, estimate the English score for a student who scored 1 in Geography?</p><p>English score = <input type="text" style="height: auto;" data-c="3"> <span class="review"></span> (note round to the nearest whole number)</p><p>d) Should we consider the answer to the above question valid? <input type="text" style="height: auto;" data-c="N"> <span class="review"></span> (Y or N)</p></div><div class="q-explanation"><p>a) b) Using lists on the stats menu of your calculator. NOTE TI users need to make sure you have turned catalogue on. See the calculator page for help.</p><p>c) Substitute x = 1 into y = 0.506x + 2.25</p><p>d) N - 1 is outside the range of data we had in the beginning.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p>Question 4</p><p>A student collected the ages and sprint times of 10 people to see if the was a relationshop between the two. The results are in the table below. the student thinks that people will get faster the older they are.</p><p><img alt="" src="../../files/Stats/bvd/q4.jpg" style="width: 700px; height: 94px;"></p></div><div class="q-answer"><p>a) What kind of correlation was the student expecting? Negatine (N) of Positive (P)</p><p> <input type="text" style="height: auto;" data-c="N"> <span class="review"></span> </p><p>b) Calculate the correlation coeficient for this data. r = <input type="text" style="height: auto;" data-c="-0.148"> <span class="review"></span> (3sf)</p><p>c) The student stated that their hypothesis was correct. Was this a correct conclusion? (Y or N) <input type="text" style="height: auto;" data-c="N"> <span class="review"></span> </p></div><div class="q-explanation"><p>a) Student was expecting that times would get faster (so lower numbers) as age increased. This is negatove correlation.</p><p>b) From GDC and carefully rounded</p><p>c) N - In fact the result shows no signifcant correlation, even though it was negative.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>Question 5</p><p>The following shows the results of an experiment to investigate what happens to the length of a spring as the weight attached to it is increased.</p><p style="text-align: center;"><img alt="" src="../../files/Stats/bvd/q5.jpg" style="width: 600px; height: 65px;"></p></div><div class="q-answer"><p>a) Calculate the PMCC for this data. r = <input type="text" style="height: auto;" data-c="0.966"> <span class="review"></span> </p><p>b) The equation of the regression line for this data is y = mx + c. What are the values of m and c, rounded to 3sf.</p><p>m = <input type="text" style="height: auto;" data-c="1.76"> <span class="review"></span> , c = <input type="text" style="height: auto;" data-c="8.41"> <span class="review"></span> </p><p>c) Using the rounded values for the regression line, estimate the length of the spring with a weight of 9 kg attached.</p><p>Length = <input type="text" style="height: auto;" data-c="24.3"> <span class="review"></span> (3sf)</p><p>d) Using the rounded values for the regression line, estimate the length of the spring with a weight of 17 kg attached.</p><p>Length = <input type="text" style="height: auto;" data-c="38.3"> <span class="review"></span> (3sf)</p><p>e) Using the rounded values for the regression line, estimate the length of the weight required to stretch the spring to a length of 17cm</p><p>Weight = <input type="text" style="height: auto;" data-c="4.88"> <span class="review"></span> (3sf)</p></div><div class="q-explanation"><p>a) From GDC</p><p>b) From GDC</p><p>c) d) For the next 2 parts it might be wise to enter y = 1.76x + 8.41 into the table function and read from the table when x is 9 and 17 respectively.</p><p>e) For this part, you could plot the function y = 1.76x + 8.41 and then solve for y = 17</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p>For a given winter, a householder compared the average monthly temperature with the volume of wood that was used for heating. The results are as follows.</p><p style="text-align: center;"><img alt="" src="../../files/Stats/bvd/q6.jpg" style="width: 700px; height: 107px;"></p></div><div class="q-answer"><p>a) What type of correlation might the householder be expecting. Negative (N) or Positive (P)</p><p> <input type="text" style="height: auto;" data-c="N"> <span class="review"></span> </p><p>b) Work out the PMCC for this data. r = <input type="text" style="height: auto;" data-c="-0.985"> <span class="review"></span> (3sf)</p><p>c) The equation of the regression line for this data is y = mx + c. What are the values of m and c, rounded to 3sf.</p><p>m = <input type="text" style="height: auto;" data-c="-0.115"> <span class="review"></span> , c = <input type="text" style="height: auto;" data-c="1.24"> <span class="review"></span> </p><p>d) The expected average temperature for the coming month is 7°. Use the rounded answers to the question abouve to predict the volume of wood that might get used. Volume = <input type="text" style="height: auto;" data-c="0.435"> <span class="review"></span> m<sup>3</sup></p><p>e) What are the mean values of the two variables? (3sf)</p><p>Mean (Ave temp) = <input type="text" style="height: auto;" data-c="2.33"> <span class="review"></span> ° (3sf), Mean (Volume) = <input type="text" style="height: auto;" data-c="0.967"> <span class="review"></span> m<sup>3</sup></p></div><div class="q-explanation"><p>a) It is reasonable to expect that as temperature falls, the volume of wood used increases - thus negative correlation.</p><p>b) c) From GDC</p><p>d) Using the function y = -0.115x + 1.24, read from the table or solve when x = 7.</p><p>e) From GDC. This point is needed to plot the regression line on paper. The other is the y - intercept. After which the line can drawn.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="totals"><span class="score"></span><button class="btn btn-success btn-block text-center check-total"><i class="fa fa-check-square-o"></i> Check</button></div></div><hr> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam Style Questions</p> </div> </div> <div class="panel-body"> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <p style="text-align: center;"><img alt="" src="../../files/Stats/bvd/bvq1.jpg" style="width: 700px; height: 438px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/671688728"></iframe></div> <p>Worked Solution</p> <p style="text-align: center;"><img alt="" src="../../files/Stats/bvd/bvq1a1.jpg" style="width: 700px; height: 505px;"></p> <p style="text-align: center;"><img alt="" src="../../files/Stats/bvd/bvq1a2.jpg" style="width: 700px; height: 508px;"> </p> </section> </div> </div> <div class="panel panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <div> <p><img alt="" src="../../images/dans-images/linear_exquestion.png" style="width: 650px; height: 374px;"></p> </div> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center"><iframe allowfullscreen="" frameborder="0" height="auto" mozallowfullscreen="" src="https://player.vimeo.com/video/675619538" webkitallowfullscreen="" width="100%"></iframe> </p> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../images/dans-images/bivariate_exqu2.png" style="width: 650px; height: 379px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/676876057"></iframe></div> </section> <div class="panel panel-default panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 4</p> </div> </div> <div class="panel-body"> <div> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">Mikel believes there is a linear relationship between time spent studying and performance in an IB exam.To test this, he collected data on ten of his classmates. He recorded the time spent studying, x, alongside the percentage they received in their most recent exam, y. </span></p> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">The following table shows the data he found. </span></p> <table align="left" dir="ltr"> <colgroup> <col> <col> <col> <col> <col> <col> <col> <col> <col> <col> <col> </colgroup> <tbody> <tr> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">Hours studying, x. </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">4 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45"> 5 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">4 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">3 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">7 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">2 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">7 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">9 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">10 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">11</span></p> </td> </tr> <tr> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">Percentage Score, y</span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">58</span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">60 </span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">43</span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">40</span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">65</span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">35</span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">70</span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">75</span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">75</span></p> </td> <td> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">80</span></p> </td> </tr> </tbody> </table> <div style="clear:both;"> </div> <p dir="ltr" role="presentation"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">a. Why does Pearson’s Product Moment Correlation Coefficient appear to be valid for this data?</span></p> <p dir="ltr" role="presentation"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">b. Find the value of Pearson’s Product Moment Correlation Coefficient, r. </span></p> <p dir="ltr" role="presentation"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">c. Comment on the strength of the correlation</span></p> <p dir="ltr"><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45">Mikel decides to study for 8 hours for the test. </span><span id="docs-internal-guid-444222c6-7fff-c87d-1fe8-ed9f4f8b0d45"></span></p> <p dir="ltr"><span>d. By using the equation of the regression line, what score could he expect to get?</span></p> <p dir="ltr"> </p> <p>Video Solution</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </p> <p> </p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> <p> </p> <div class="panel-footer"> <div> </div> </div> </div> <p><span id="cke_bm_805E" style="display: none;"> </span></p> <div class="page-container panel-self-assessment" data-id="2266"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>4.4 Bivariate data & Linear Correlation</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" 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