{"id":105,"date":"2021-01-12T22:19:50","date_gmt":"2021-01-12T22:19:50","guid":{"rendered":"https:\/\/textbooks.jaykesler.net\/introstats\/chapter\/scatter-plots\/"},"modified":"2023-04-19T20:29:56","modified_gmt":"2023-04-19T20:29:56","slug":"scatter-plots","status":"publish","type":"chapter","link":"https:\/\/textbooks.jaykesler.net\/introstats\/chapter\/scatter-plots\/","title":{"rendered":"Scatter Plots"},"content":{"raw":"\r\n[latexpage]\r\n<\/span>\r\n
\r\n

Before we take up the discussion of linear regression and correlation, we need to examine a way to display the relation between two variables x<\/em> and y<\/em>. The most common and easiest way is a scatter plot<\/strong>. The following example illustrates a scatter plot.<\/p>\r\n\r\n

\r\n

Example <\/span>12.5<\/span><\/h3>\r\n<\/header>
\r\n
\r\n

In Europe and Asia, m-commerce is popular. M-commerce users have special mobile phones that work like electronic wallets as well as provide phone and Internet services. Users can do everything from paying for parking to buying a TV set or soda from a machine to banking to checking sports scores on the Internet. For the years 2000 through 2004, was\r\nthere a relationship between the year and the number of m-commerce users? Construct a scatter plot. Let x<\/em> = the year and let y<\/em> = the number of m-commerce users, in millions.<\/p>\r\n\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Table showing the number of m-commerce users (in millions) by year.<\/caption>\r\n
$x$ (year)<\/th>\r\n$y$ (# of users)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
2000<\/td>\r\n0.5<\/td>\r\n<\/tr>\r\n
2002<\/td>\r\n20.0<\/td>\r\n<\/tr>\r\n
2003<\/td>\r\n33.0<\/td>\r\n<\/tr>\r\n
2004<\/td>\r\n47.0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
Table <\/span>12.1<\/span><\/div>\r\n<\/div>\r\n
\r\n
\"This<\/span><\/figure>\r\n
Figure <\/span>12.5<\/span> Scatter plot showing the number of m-commerce users (in millions) by year.<\/span><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
\r\n

Try It <\/span>12.5<\/span><\/h3>\r\n<\/header>
\r\n
<\/header>
\r\n
\r\n
\r\n

Amelia plays basketball for her high school. She wants to improve to play at the college level. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data:<\/p>\r\n\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
X<\/em> (hours practicing jump shot)<\/th>\r\nY<\/em> (points scored in a game)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
5<\/td>\r\n15<\/td>\r\n<\/tr>\r\n
7<\/td>\r\n22<\/td>\r\n<\/tr>\r\n
9<\/td>\r\n28<\/td>\r\n<\/tr>\r\n
10<\/td>\r\n31<\/td>\r\n<\/tr>\r\n
11<\/td>\r\n33<\/td>\r\n<\/tr>\r\n
12<\/td>\r\n36<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
Table <\/span>12.2<\/span><\/div>\r\n<\/div>\r\n

Construct a scatter plot and state if what Amelia thinks appears to be true.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section><\/div>\r\n

A scatter plot shows the direction<\/strong> of a relationship between the variables. A clear direction happens when there is either:<\/p>\r\n\r\n

    \r\n \t
  • High values of one variable occurring with high values of the other variable or low values of one variable occurring with low values of the other variable.<\/li>\r\n \t
  • High values of one variable occurring with low values of the other variable.<\/li>\r\n<\/ul>\r\n

    You can determine the strength<\/strong> of the relationship by looking at the scatter plot and seeing how close the points are to a line, a power function, an exponential function,\r\nor to some other type of function. For a linear relationship there is an exception. Consider a scatter plot where all the points fall on a horizontal line providing a \"perfect fit.\" The horizontal line would in fact show no relationship.<\/p>\r\n

    When you look at a scatterplot, you want to notice the overall pattern<\/strong> and any deviations<\/strong> from the pattern. The following scatterplot examples illustrate these concepts.<\/p>\r\n\r\n

    \r\n
    \"The<\/span><\/figure>\r\n
    Figure <\/span>12.6<\/span><\/div>\r\n<\/div>\r\n
    \r\n
    \"The<\/span><\/figure>\r\n
    Figure <\/span>12.7<\/span><\/div>\r\n<\/div>\r\n
    \r\n
    \r\n\"The\r\n<\/span><\/figure>\r\n
    Figure <\/span>12.8<\/span><\/div>\r\n<\/div>\r\n

    In this chapter, we are interested in scatter plots that show a linear pattern. Linear patterns are quite common. The linear relationship is strong if the points are close to a straight line, except in the case of a horizontal line where there is no relationship. If we think that the points show a linear relationship, we would like to draw a line on the scatter plot. This line can be calculated through a process called linear regression<\/span>. However, we only calculate a regression line if one of the variables helps to explain or predict the other variable. If x<\/em> is the independent variable and y<\/em> the dependent variable,\r\nthen we can use a regression line to predict y<\/em> for a given value of x<\/em><\/p>\r\n\r\n<\/div>","rendered":"


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

    \n

    Before we take up the discussion of linear regression and correlation, we need to examine a way to display the relation between two variables x<\/em> and y<\/em>. The most common and easiest way is a scatter plot<\/strong>. The following example illustrates a scatter plot.<\/p>\n

    \n
    \n

    Example <\/span>12.5<\/span><\/h3>\n<\/header>\n
    \n
    \n

    In Europe and Asia, m-commerce is popular. M-commerce users have special mobile phones that work like electronic wallets as well as provide phone and Internet services. Users can do everything from paying for parking to buying a TV set or soda from a machine to banking to checking sports scores on the Internet. For the years 2000 through 2004, was
    \nthere a relationship between the year and the number of m-commerce users? Construct a scatter plot. Let x<\/em> = the year and let y<\/em> = the number of m-commerce users, in millions.<\/p>\n

    \n\n\n\n\n\n\n\n\n
    Table showing the number of m-commerce users (in millions) by year.<\/caption>\n
    $x$ (year)<\/th>\n$y$ (# of users)<\/th>\n<\/tr>\n<\/thead>\n
    2000<\/td>\n0.5<\/td>\n<\/tr>\n
    2002<\/td>\n20.0<\/td>\n<\/tr>\n
    2003<\/td>\n33.0<\/td>\n<\/tr>\n
    2004<\/td>\n47.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
    Table <\/span>12.1<\/span><\/div>\n<\/div>\n
    \n
    \"This<\/span><\/figure>\n
    Figure <\/span>12.5<\/span> Scatter plot showing the number of m-commerce users (in millions) by year.<\/span><\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n
    \n
    \n

    Try It <\/span>12.5<\/span><\/h3>\n<\/header>\n
    \n
    \n
    <\/header>\n
    \n
    \n
    \n

    Amelia plays basketball for her high school. She wants to improve to play at the college level. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data:<\/p>\n

    \n\n\n\n\n\n\n\n\n\n\n
    X<\/em> (hours practicing jump shot)<\/th>\nY<\/em> (points scored in a game)<\/th>\n<\/tr>\n<\/thead>\n
    5<\/td>\n15<\/td>\n<\/tr>\n
    7<\/td>\n22<\/td>\n<\/tr>\n
    9<\/td>\n28<\/td>\n<\/tr>\n
    10<\/td>\n31<\/td>\n<\/tr>\n
    11<\/td>\n33<\/td>\n<\/tr>\n
    12<\/td>\n36<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
    Table <\/span>12.2<\/span><\/div>\n<\/div>\n

    Construct a scatter plot and state if what Amelia thinks appears to be true.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/section>\n<\/div>\n

    A scatter plot shows the direction<\/strong> of a relationship between the variables. A clear direction happens when there is either:<\/p>\n

      \n
    • High values of one variable occurring with high values of the other variable or low values of one variable occurring with low values of the other variable.<\/li>\n
    • High values of one variable occurring with low values of the other variable.<\/li>\n<\/ul>\n

      You can determine the strength<\/strong> of the relationship by looking at the scatter plot and seeing how close the points are to a line, a power function, an exponential function,
      \nor to some other type of function. For a linear relationship there is an exception. Consider a scatter plot where all the points fall on a horizontal line providing a “perfect fit.” The horizontal line would in fact show no relationship.<\/p>\n

      When you look at a scatterplot, you want to notice the overall pattern<\/strong> and any deviations<\/strong> from the pattern. The following scatterplot examples illustrate these concepts.<\/p>\n

      \n
      \"The<\/span><\/figure>\n
      Figure <\/span>12.6<\/span><\/div>\n<\/div>\n
      \n
      \"The<\/span><\/figure>\n
      Figure <\/span>12.7<\/span><\/div>\n<\/div>\n
      \n

      \n\"The
      \n<\/span><\/figure>\n
      Figure <\/span>12.8<\/span><\/div>\n<\/div>\n

      In this chapter, we are interested in scatter plots that show a linear pattern. Linear patterns are quite common. The linear relationship is strong if the points are close to a straight line, except in the case of a horizontal line where there is no relationship. If we think that the points show a linear relationship, we would like to draw a line on the scatter plot. This line can be calculated through a process called linear regression<\/span>. However, we only calculate a regression line if one of the variables helps to explain or predict the other variable. If x<\/em> is the independent variable and y<\/em> the dependent variable,
      \nthen we can use a regression line to predict y<\/em> for a given value of x<\/em><\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-105","chapter","type-chapter","status-publish","hentry"],"part":103,"_links":{"self":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/chapters\/105","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":4,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/chapters\/105\/revisions"}],"predecessor-version":[{"id":589,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/chapters\/105\/revisions\/589"}],"part":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/parts\/103"}],"metadata":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/chapters\/105\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/wp\/v2\/media?parent=105"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/pressbooks\/v2\/chapter-type?post=105"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/wp\/v2\/contributor?post=105"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/textbooks.jaykesler.net\/introstats\/wp-json\/wp\/v2\/license?post=105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}