{"id":2100,"date":"2022-01-26T23:31:37","date_gmt":"2022-01-26T23:31:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=2100"},"modified":"2022-02-01T23:19:12","modified_gmt":"2022-02-01T23:19:12","slug":"16a","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/16a\/","title":{"raw":"16A","rendered":"16A"},"content":{"raw":"<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Skill or Concept: I can . . .<\/td>\r\n<td>Questions to check your understanding<\/td>\r\n<td>Rating\r\nfrom 1 to 5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify the difference between the sample slope of the line of best fit and the population slope.<\/td>\r\n<td>4<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Understand the relationship between the correlation coefficient and the slope of a regression line.<\/td>\r\n<td>1\u20133<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the hypotheses and obtain a test statistic and P-value for a test for significance of slope.<\/td>\r\n<td>5 and 6<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img class=\"alignnone wp-image-2101\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232404\/Picture75-300x96.png\" alt=\"A scatterplot labeled \u201cTemperature\u201d on the x-axis and \u201cPark Attendance\u201d on the y-axis. There is a line of best fit that extends from approximately (70, 12500) to approximately (105, 13000). The points near the middle of the x-axis are generally higher in value than those near either end.\" width=\"1216\" height=\"389\" \/> <img class=\"alignnone wp-image-2102\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232409\/Picture762-300x205.jpg\" alt=\"An illustration of a city.\" width=\"945\" height=\"646\" \/> <img class=\"alignnone wp-image-2103\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232413\/Picture771-300x87.png\" alt=\"A residual plot labeled \u201cSize\u201d on the x-axis and \u201cResidual\u201d on the y-axis. There is a horizontal line at y = 0. The points with lower x-values are generally closer to the line than those with higher x-values.\" width=\"1245\" height=\"361\" \/> <img class=\"alignnone wp-image-2104\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232417\/Picture781-300x112.png\" alt=\"A scatterplot labeled \u201cSquare Feet\u201d on the x-axis and \u201cPrice\u201d on the y-axis. There is a line of best fit that extends approximately from (1300, 175000) to (3200, 390000). The points are clustered near the line.\" width=\"948\" height=\"354\" \/> <img class=\"alignnone wp-image-2105\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232421\/Picture791-300x93.png\" alt=\"A residual plot labeled \u201cSquare Feet\u201d on the x-axis and \u201cResidual\u201d on the y-axis. There is a horizontal line at y = 0. There is no pattern to the points.\" width=\"1171\" height=\"363\" \/> <img class=\"alignnone wp-image-2106\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232426\/Picture801-300x76.png\" alt=\"A table labeled &quot;Linear Regression Equation,&quot; with headings &quot;Parameter,&quot; &quot;Estimate,&quot; &quot;Standard Error,&quot; &quot;t Statistic,&quot; and &quot;P-value.&quot; The first row has values &quot;intercept,&quot; 44,321, 12,357, 3.59, and 0.001. The second row has values &quot;Slope (Square Feet),&quot; 108.1, 5.808, 18.62, and &lt;0.0001.\" width=\"947\" height=\"240\" \/> <img class=\"alignnone wp-image-2107\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232430\/Picture813-300x95.png\" alt=\"A scatterplot labeled \u201cAge (years)\u201d on the x-axis and \u201cHours of Sleep in a Typical Night\u201d on the y-axis. The points near the middle of the x-axis are generally lower in value than those near either end. \" width=\"1247\" height=\"395\" \/> <img class=\"alignnone wp-image-2108\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232435\/Picture822-300x84.png\" alt=\"A residual plot labeled \u201cResidual\u201d on the y-axis. There is a horizontal line at y = 0. The points near the middle of the x-axis are generally lower in value than those near either end.\" width=\"943\" height=\"264\" \/> <img class=\"alignnone wp-image-2109\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232439\/Picture832-300x142.png\" alt=\"A scatterplot labeled \u201cMilk\u201d on the x-axis and \u201cEggs\u201d on the y-axis. There is a line whose equation is given at the top, where it reads \u201cRegression Line y = -0.79 + 0.76.\u201d Beneath the graph is a table titled \u201cLinear Regression Equation,\u201d with columns \u201cParameter,\u201d \u201cEstimate,\u201d \u201cStandard Error,\u201d \u201ct Statistic,\u201d and \u201cP-value.\u201d The first row has values \u201cIntercept,\u201d -0.7895, 0.659, -1.2, 0.2456. The second row has values \u201cSlope (Milk),\u201d 0.7595, 0.2049, 3.71, 0.0015.\" width=\"1246\" height=\"590\" \/> <img class=\"alignnone wp-image-2110\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232444\/Picture842-300x84.png\" alt=\"A residual plot labeled \u201cMilk\u201d on the x-axis and \u201cResidual\u201d on the y-axis. There is a horizontal line at y = 0. The points have no pattern.\" width=\"943\" height=\"264\" \/> <img class=\"alignnone wp-image-2111\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232447\/Picture852-300x92.png\" alt=\"A scatterplot labeled \u201cWeight (kg)\u201d on the x-axis and \u201cGas Mileage (mpg)\u201d on the y-axis. There is a line that extends approximately from (2500, 33) to (6400, 13). The points are close to the line.\" width=\"1073\" height=\"329\" \/> <img class=\"alignnone wp-image-2112\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232451\/Picture861-300x88.png\" alt=\"A scatterplot labeled \u201cSteady Driving Speed (mph)\u201d on the x-axis and \u201cFuel Efficiency (mpg)\u201d on the y-axis. There is a line that extends approximately from (5, 31) to (85, 34). The points near the middle of the x-axis are generally higher in value than those near either end.\" width=\"934\" height=\"274\" \/> <img class=\"alignnone wp-image-2113\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232456\/Picture872-300x102.png\" alt=\"A scatterplot titled \u201cSodium and Sugar Content of 20 Cereals.\u201d The x-axis is labeled \u201cSugar (g)\u201d and the y-axis is titled \u201cSodium (mg).\u201d There is a pin that appears horizontal at approximately y = 170. Most points are relatively close to the line.\" width=\"1244\" height=\"423\" \/> <img class=\"alignnone wp-image-2114\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232500\/Picture882-300x283.png\" alt=\"A selection menu. The first heading reads \u201cPlot Options\u201d and has checkboxes for \u201cSmooth Trend,\u201d \u201cRegression Line,\u201d \u201cClick to Remove Points,\u201d \u201cSelect Variable(s) for Hover Info,\u201d \u201cTitle &amp; Subtitle,\u201d \u201cDrag Points,\u201d and \u201cAxis Labels.\u201d Only \u201cRegression Line\u201d is selected. The next heading reads \u201cRegression Options\u201d and has checkboxes for \u201cFind Predicted Value,\u201d \u201cShow Residuals on Plot,\u201d \u201cShow Standard Errors &amp; P-values,\u201d \u201cConfidence Interval for Slope,\u201d \u201cConfidence\/Prediction Interval,\u201d and \u201cANOVA Table.\u201d Only \u201cShow Standard Errors &amp; P-values\u201d is selected.\" width=\"917\" height=\"865\" \/>\r\n\r\n<\/div>","rendered":"<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td>Skill or Concept: I can . . .<\/td>\n<td>Questions to check your understanding<\/td>\n<td>Rating<br \/>\nfrom 1 to 5<\/td>\n<\/tr>\n<tr>\n<td>Identify the difference between the sample slope of the line of best fit and the population slope.<\/td>\n<td>4<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Understand the relationship between the correlation coefficient and the slope of a regression line.<\/td>\n<td>1\u20133<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write the hypotheses and obtain a test statistic and P-value for a test for significance of slope.<\/td>\n<td>5 and 6<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2101\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232404\/Picture75-300x96.png\" alt=\"A scatterplot labeled \u201cTemperature\u201d on the x-axis and \u201cPark Attendance\u201d on the y-axis. There is a line of best fit that extends from approximately (70, 12500) to approximately (105, 13000). The points near the middle of the x-axis are generally higher in value than those near either end.\" width=\"1216\" height=\"389\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2102\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232409\/Picture762-300x205.jpg\" alt=\"An illustration of a city.\" width=\"945\" height=\"646\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2103\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232413\/Picture771-300x87.png\" alt=\"A residual plot labeled \u201cSize\u201d on the x-axis and \u201cResidual\u201d on the y-axis. There is a horizontal line at y = 0. The points with lower x-values are generally closer to the line than those with higher x-values.\" width=\"1245\" height=\"361\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2104\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232417\/Picture781-300x112.png\" alt=\"A scatterplot labeled \u201cSquare Feet\u201d on the x-axis and \u201cPrice\u201d on the y-axis. There is a line of best fit that extends approximately from (1300, 175000) to (3200, 390000). The points are clustered near the line.\" width=\"948\" height=\"354\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2105\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232421\/Picture791-300x93.png\" alt=\"A residual plot labeled \u201cSquare Feet\u201d on the x-axis and \u201cResidual\u201d on the y-axis. There is a horizontal line at y = 0. There is no pattern to the points.\" width=\"1171\" height=\"363\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2106\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232426\/Picture801-300x76.png\" alt=\"A table labeled &quot;Linear Regression Equation,&quot; with headings &quot;Parameter,&quot; &quot;Estimate,&quot; &quot;Standard Error,&quot; &quot;t Statistic,&quot; and &quot;P-value.&quot; The first row has values &quot;intercept,&quot; 44,321, 12,357, 3.59, and 0.001. The second row has values &quot;Slope (Square Feet),&quot; 108.1, 5.808, 18.62, and &lt;0.0001.\" width=\"947\" height=\"240\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2107\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232430\/Picture813-300x95.png\" alt=\"A scatterplot labeled \u201cAge (years)\u201d on the x-axis and \u201cHours of Sleep in a Typical Night\u201d on the y-axis. The points near the middle of the x-axis are generally lower in value than those near either end.\" width=\"1247\" height=\"395\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2108\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232435\/Picture822-300x84.png\" alt=\"A residual plot labeled \u201cResidual\u201d on the y-axis. There is a horizontal line at y = 0. The points near the middle of the x-axis are generally lower in value than those near either end.\" width=\"943\" height=\"264\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2109\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232439\/Picture832-300x142.png\" alt=\"A scatterplot labeled \u201cMilk\u201d on the x-axis and \u201cEggs\u201d on the y-axis. There is a line whose equation is given at the top, where it reads \u201cRegression Line y = -0.79 + 0.76.\u201d Beneath the graph is a table titled \u201cLinear Regression Equation,\u201d with columns \u201cParameter,\u201d \u201cEstimate,\u201d \u201cStandard Error,\u201d \u201ct Statistic,\u201d and \u201cP-value.\u201d The first row has values \u201cIntercept,\u201d -0.7895, 0.659, -1.2, 0.2456. The second row has values \u201cSlope (Milk),\u201d 0.7595, 0.2049, 3.71, 0.0015.\" width=\"1246\" height=\"590\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2110\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232444\/Picture842-300x84.png\" alt=\"A residual plot labeled \u201cMilk\u201d on the x-axis and \u201cResidual\u201d on the y-axis. There is a horizontal line at y = 0. The points have no pattern.\" width=\"943\" height=\"264\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2111\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232447\/Picture852-300x92.png\" alt=\"A scatterplot labeled \u201cWeight (kg)\u201d on the x-axis and \u201cGas Mileage (mpg)\u201d on the y-axis. There is a line that extends approximately from (2500, 33) to (6400, 13). The points are close to the line.\" width=\"1073\" height=\"329\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2112\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232451\/Picture861-300x88.png\" alt=\"A scatterplot labeled \u201cSteady Driving Speed (mph)\u201d on the x-axis and \u201cFuel Efficiency (mpg)\u201d on the y-axis. There is a line that extends approximately from (5, 31) to (85, 34). The points near the middle of the x-axis are generally higher in value than those near either end.\" width=\"934\" height=\"274\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2113\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232456\/Picture872-300x102.png\" alt=\"A scatterplot titled \u201cSodium and Sugar Content of 20 Cereals.\u201d The x-axis is labeled \u201cSugar (g)\u201d and the y-axis is titled \u201cSodium (mg).\u201d There is a pin that appears horizontal at approximately y = 170. Most points are relatively close to the line.\" width=\"1244\" height=\"423\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2114\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5738\/2022\/01\/26232500\/Picture882-300x283.png\" alt=\"A selection menu. The first heading reads \u201cPlot Options\u201d and has checkboxes for \u201cSmooth Trend,\u201d \u201cRegression Line,\u201d \u201cClick to Remove Points,\u201d \u201cSelect Variable(s) for Hover Info,\u201d \u201cTitle &amp; Subtitle,\u201d \u201cDrag Points,\u201d and \u201cAxis Labels.\u201d Only \u201cRegression Line\u201d is selected. The next heading reads \u201cRegression Options\u201d and has checkboxes for \u201cFind Predicted Value,\u201d \u201cShow Residuals on Plot,\u201d \u201cShow Standard Errors &amp; P-values,\u201d \u201cConfidence Interval for Slope,\u201d \u201cConfidence\/Prediction Interval,\u201d and \u201cANOVA Table.\u201d Only \u201cShow Standard Errors &amp; P-values\u201d is selected.\" width=\"917\" height=\"865\" \/><\/p>\n<\/div>\n","protected":false},"author":23592,"menu_order":55,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2100","chapter","type-chapter","status-publish","hentry"],"part":704,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/2100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/2100\/revisions"}],"predecessor-version":[{"id":2653,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/2100\/revisions\/2653"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/704"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/2100\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=2100"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=2100"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=2100"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=2100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}