{"id":5545,"date":"2022-09-21T17:05:05","date_gmt":"2022-09-21T17:05:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5545"},"modified":"2022-10-17T16:56:50","modified_gmt":"2022-10-17T16:56:50","slug":"17a-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/17a-coreq\/","title":{"raw":"17A Coreq","rendered":"17A Coreq"},"content":{"raw":"
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In the next preview assignment and in the next class, you will need to be able to identify response and explanatory variables, check assumptions with residual plots, write a simple linear regression equation, interpret a regression coefficient in the context of the data, and interpret the coefficient of determination.<\/div>\r\n
Review of Simple Linear Regression Students in an introductory statistics class at The University of Queensland participated in a simple experiment.[footnote]Wilson, R. J. (n.d.). Pulse rates before and after exercise. StatSci.org.http:\/\/www.statsci.org\/data\/oz\/ms212.html[\/footnote] The students took their own pulse rates. They were then asked to flip a coin. If the coin came up heads, they were to run in place for one minute. Otherwise, they sat for one minute. Afterward, everyone took their pulse rates again. The pulse rates and other physiological and lifestyle data were recorded in a dataset called \u201cPulseRate.\u201d The variables in the dataset are:<\/div>\r\n<\/div>\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\r\n\r\n\r\n\r\n
Variable<\/strong><\/td>\r\nDescription<\/strong><\/td>\r\n<\/tr>\r\n
ID<\/em><\/td>\r\nIdentification number<\/td>\r\n<\/tr>\r\n
Height<\/em><\/td>\r\nHeight in centimeters (cm)<\/td>\r\n<\/tr>\r\n
Weight<\/em><\/td>\r\nWeight in kilograms (kg)<\/td>\r\n<\/tr>\r\n
Age<\/em><\/td>\r\nAge in years<\/td>\r\n<\/tr>\r\n
Sex<\/em><\/td>\r\nMale\/female<\/td>\r\n<\/tr>\r\n
Smokes<\/em><\/td>\r\nAre you a regular smoker? (yes\/no)<\/td>\r\n<\/tr>\r\n
Alcohol<\/em><\/td>\r\nAre you a regular drinker? (yes\/no)<\/td>\r\n<\/tr>\r\n
Exercise<\/em><\/td>\r\nWhat is your frequency of exercise? (low, moderate, high)<\/td>\r\n<\/tr>\r\n
GroupAssignment<\/em><\/td>\r\nWhether the student ran or sat between the first and second pulse measurements<\/td>\r\n<\/tr>\r\n
Pulse1<\/em><\/td>\r\nFirst pulse measurement (rate per minute)<\/td>\r\n<\/tr>\r\n
Pulse2<\/em><\/td>\r\nSecond pulse measurement (rate per minute)<\/td>\r\n<\/tr>\r\n
Year<\/em><\/td>\r\nYear of class (1993\u20131998)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n
We will be investigating pulse rate in the preview assignment. In this corequisite support activity, we will focus on a different investigative question\u2014the students are interested in building a model that can be used to estimate a student\u2019s weight based on the student\u2019s height. To complete this support activity, you will need to access the DCMPLinear Regression tool at https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/. You will also need to upload spreadsheet DCMP_STAT_17A_PulseRate into the data analysis tool. To upload a dataset, select \u201cUpload File\u201d under \u201cEnter Data.\u201dThen, click \u201cBrowse\u201dto find the location of the file on your computer and click \u201cOpen.\u201d The dataset will be uploaded into the data analysis tool.<\/div>\r\n
<\/div>\r\n
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\r\n

Question 1<\/h3>\r\n1) What arethe explanatory and response variables?\r\n\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
\r\n
\r\n

Question 2<\/h3>\r\n2) Create a scatterplot to visualize the relationship between the explanatory and response variable. Don\u2019t forget to select the explanatory variable (\ud835\udc4b)and response variable (\ud835\udc4c)in the data analysis tool.\r\n\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
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\r\n

Question 3<\/h3>\r\n3) Using the scatterplot you created in Question 2, describe the relationship between student weight and student height.\r\n\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
\r\n
\r\n

Question 4<\/h3>\r\n4) Fit a linear regression model to describe the relationship between student height andstudentweight. Calculate the line of best fit to describe the relationship between the two variablesusing the data analysis tool. What is the equation of the simple linear regression model?\r\n\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
\r\n
\r\n

Question 5<\/h3>\r\n5) Interpret the value of the slope of the line of best fit.\r\n\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
\r\n
\r\n

Question 6<\/h3>\r\n6) Create a scatterplot of the residuals vs. weight(\ud835\udc65)by selecting the Fitted Values & Residual Analysis tab. Is there anything about this residual plot that would cause you toquestion the reasonableness of fitting a linear model?\r\n\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
\r\n
\r\n

Question 7<\/h3>\r\n7) Calculate\ud835\udc452 using the data analysis tooland interpret the value.\r\n\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
\r\n
\r\n

Question 8<\/h3>\r\n8) At the 5% significance level, determine whether there is convincing evidence to conclude that there is a useful linear relationship between student height and student weight. Test the hypothesis: \ud835\udc3b0:\u03b2=0vs. \ud835\udc3b\ud835\udc34:\u03b2\u22600. Write your answer in a complete sentence and support your answer with statistical evidence.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
In the next preview assignment and in the next class, you will need to be able to identify response and explanatory variables, check assumptions with residual plots, write a simple linear regression equation, interpret a regression coefficient in the context of the data, and interpret the coefficient of determination.<\/div>\n
Review of Simple Linear Regression Students in an introductory statistics class at The University of Queensland participated in a simple experiment.[1]<\/sup><\/a> The students took their own pulse rates. They were then asked to flip a coin. If the coin came up heads, they were to run in place for one minute. Otherwise, they sat for one minute. Afterward, everyone took their pulse rates again. The pulse rates and other physiological and lifestyle data were recorded in a dataset called \u201cPulseRate.\u201d The variables in the dataset are:<\/div>\n<\/div>\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Variable<\/strong><\/td>\nDescription<\/strong><\/td>\n<\/tr>\n
ID<\/em><\/td>\nIdentification number<\/td>\n<\/tr>\n
Height<\/em><\/td>\nHeight in centimeters (cm)<\/td>\n<\/tr>\n
Weight<\/em><\/td>\nWeight in kilograms (kg)<\/td>\n<\/tr>\n
Age<\/em><\/td>\nAge in years<\/td>\n<\/tr>\n
Sex<\/em><\/td>\nMale\/female<\/td>\n<\/tr>\n
Smokes<\/em><\/td>\nAre you a regular smoker? (yes\/no)<\/td>\n<\/tr>\n
Alcohol<\/em><\/td>\nAre you a regular drinker? (yes\/no)<\/td>\n<\/tr>\n
Exercise<\/em><\/td>\nWhat is your frequency of exercise? (low, moderate, high)<\/td>\n<\/tr>\n
GroupAssignment<\/em><\/td>\nWhether the student ran or sat between the first and second pulse measurements<\/td>\n<\/tr>\n
Pulse1<\/em><\/td>\nFirst pulse measurement (rate per minute)<\/td>\n<\/tr>\n
Pulse2<\/em><\/td>\nSecond pulse measurement (rate per minute)<\/td>\n<\/tr>\n
Year<\/em><\/td>\nYear of class (1993\u20131998)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n
We will be investigating pulse rate in the preview assignment. In this corequisite support activity, we will focus on a different investigative question\u2014the students are interested in building a model that can be used to estimate a student\u2019s weight based on the student\u2019s height. To complete this support activity, you will need to access the DCMPLinear Regression tool at https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/. You will also need to upload spreadsheet DCMP_STAT_17A_PulseRate into the data analysis tool. To upload a dataset, select \u201cUpload File\u201d under \u201cEnter Data.\u201dThen, click \u201cBrowse\u201dto find the location of the file on your computer and click \u201cOpen.\u201d The dataset will be uploaded into the data analysis tool.<\/div>\n
<\/div>\n
\n
\n

Question 1<\/h3>\n

1) What arethe explanatory and response variables?<\/p>\n<\/div>\n<\/div>\n

<\/div>\n
\n
\n

Question 2<\/h3>\n

2) Create a scatterplot to visualize the relationship between the explanatory and response variable. Don\u2019t forget to select the explanatory variable (\ud835\udc4b)and response variable (\ud835\udc4c)in the data analysis tool.<\/p>\n<\/div>\n<\/div>\n

<\/div>\n
\n
\n

Question 3<\/h3>\n

3) Using the scatterplot you created in Question 2, describe the relationship between student weight and student height.<\/p>\n<\/div>\n<\/div>\n

<\/div>\n
\n
\n

Question 4<\/h3>\n

4) Fit a linear regression model to describe the relationship between student height andstudentweight. Calculate the line of best fit to describe the relationship between the two variablesusing the data analysis tool. What is the equation of the simple linear regression model?<\/p>\n<\/div>\n<\/div>\n

<\/div>\n
\n
\n

Question 5<\/h3>\n

5) Interpret the value of the slope of the line of best fit.<\/p>\n<\/div>\n<\/div>\n

<\/div>\n
\n
\n

Question 6<\/h3>\n

6) Create a scatterplot of the residuals vs. weight(\ud835\udc65)by selecting the Fitted Values & Residual Analysis tab. Is there anything about this residual plot that would cause you toquestion the reasonableness of fitting a linear model?<\/p>\n<\/div>\n<\/div>\n

<\/div>\n
\n
\n

Question 7<\/h3>\n

7) Calculate\ud835\udc452 using the data analysis tooland interpret the value.<\/p>\n<\/div>\n<\/div>\n

<\/div>\n
\n
\n

Question 8<\/h3>\n

8) At the 5% significance level, determine whether there is convincing evidence to conclude that there is a useful linear relationship between student height and student weight. Test the hypothesis: \ud835\udc3b0:\u03b2=0vs. \ud835\udc3b\ud835\udc34:\u03b2\u22600. Write your answer in a complete sentence and support your answer with statistical evidence.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

  1. Wilson, R. J. (n.d.). Pulse rates before and after exercise. StatSci.org.http:\/\/www.statsci.org\/data\/oz\/ms212.html ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":23592,"menu_order":1,"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-5545","chapter","type-chapter","status-publish","hentry"],"part":5543,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5545","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\/5545\/revisions"}],"predecessor-version":[{"id":5649,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5545\/revisions\/5649"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5543"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5545\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5545"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5545"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5545"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}