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Chapter 1. 3 Notes and Examples In statistics, linear regression is a linear approach to modeling the relationship between a scalar response (or dependent variable, ‘y’ ) and one or more explanatory variables (or independent variables. ‘ x ‘ ). The case of one explanatory variable is called simple linear regression. 0.70 < r="">< 1="" -0.70="">< r="">< -1="" r="">< 0.50 entering data into the ti 84 graphic calculator : press stat , edit, enter x values into l1 and y values into l2 press stat , calc, 4linreg, enter ,enter { a = slope , b = y-intercept , r is the correlation coefficient ( gives you the strength among the depend and independent variables , r2 is the coefficient of determination (what % of the line can be explained ) examples 1.3 1. the following table show the percentage of male smokers from 2000 until 2016. note : you have to change the actual years to ‘ code years’ when entering the data into the calculator.. the time starts at the year 2000,therefore 2000 = ‘code year ‘ 0. the year 2007 is ‘code year’ 7 and so on. year male % 2000 20.1 2007 22.9 2008 24.4 20010 24.9 2012 25.7 2015 26.0 2016 26.8 find the liner regression model. interpret the slope and the y-intercept. by using your equation from the previous part, predict the percentage of smokers for 2019. calculate the correlation coefficient ( r ) explain the meaning. (relationship) calculate the coefficient of determination . explain the meaning. .2. given the following table : x y 1 3 2 3 3 3 4 4 5 8 find the linear regression model. by using your equation from the previous part, predict the value of x when y = 9 calculate the correlation coefficient ( r ) explain the meaning. (relationship) calculate the coefficient of determination . explain the meaning. 3. the following table show information on the conditions of demand and supply for designer purses, where the quantity of designer purses is measured in thousands. ( use ti 84) price quantity demanded quantity supplied $700 405 525 $900 325 655 hint: use ( quantity, price ) a. ) write and equation for the supply . b. ) write an equation for the demand . c. find the equilibrium quantity and price. 0.50="" entering="" data="" into="" the="" ti="" 84="" graphic="" calculator="" :="" press="" stat="" ,="" edit,="" enter="" x="" values="" into="" l1="" and="" y="" values="" into="" l2="" press="" stat="" ,="" calc,="" 4linreg,="" enter="" ,enter="" {="" a="slope" ,="" b="y-intercept" ,="" r="" is="" the="" correlation="" coefficient="" (="" gives="" you="" the="" strength="" among="" the="" depend="" and="" independent="" variables="" ,="" r2="" is="" the="" coefficient="" of="" determination="" (what="" %="" of="" the="" line="" can="" be="" explained="" )="" examples="" 1.3="" 1.="" the="" following="" table="" show="" the="" percentage="" of="" male="" smokers="" from="" 2000="" until="" 2016.="" note="" :="" you="" have="" to="" change="" the="" actual="" years="" to="" ‘="" code="" years’="" when="" entering="" the="" data="" into="" the="" calculator..="" the="" time="" starts="" at="" the="" year="" 2000,therefore="" 2000="‘code" year="" ‘="" 0.="" the="" year="" 2007="" is="" ‘code="" year’="" 7="" and="" so="" on.="" year="" male="" %="" 2000="" 20.1="" 2007="" 22.9="" 2008="" 24.4="" 20010="" 24.9="" 2012="" 25.7="" 2015="" 26.0="" 2016="" 26.8="" find="" the="" liner="" regression="" model.="" interpret="" the="" slope="" and="" the="" y-intercept.="" by="" using="" your="" equation="" from="" the="" previous="" part,="" predict="" the="" percentage="" of="" smokers="" for="" 2019.="" calculate="" the="" correlation="" coefficient="" (="" r="" )="" explain="" the="" meaning.="" (relationship)="" calculate="" the="" coefficient="" of="" determination="" .="" explain="" the="" meaning.="" .2.="" given="" the="" following="" table="" :="" x="" y="" 1="" 3="" 2="" 3="" 3="" 3="" 4="" 4="" 5="" 8="" find="" the="" linear="" regression="" model.="" by="" using="" your="" equation="" from="" the="" previous="" part,="" predict="" the="" value="" of="" x="" when="" y="9" calculate="" the="" correlation="" coefficient="" (="" r="" )="" explain="" the="" meaning.="" (relationship)="" calculate="" the="" coefficient="" of="" determination="" .="" explain="" the="" meaning.="" 3.="" the="" following="" table="" show="" information="" on="" the="" conditions="" of="" demand="" and="" supply="" for="" designer="" purses,="" where="" the="" quantity="" of="" designer="" purses="" is="" measured="" in="" thousands.="" (="" use="" ti="" 84)="" price="" quantity="" demanded="" quantity="" supplied="" $700="" 405="" 525="" $900="" 325="" 655="" hint:="" use="" (="" quantity,="" price="" )="" a.="" )="" write="" and="" equation="" for="" the="" supply="" .="" b.="" )="" write="" an="" equation="" for="" the="" demand="" .="" c.="" find="" the="" equilibrium="" quantity="" and="">