MPM1D: Line of Best Fit



5152179-75120500“Youth are out of control. The Youth Justice Act is too lenient. We need to crack down on this growing epidemic of youth violence against people and property. We need to get tough.” Or so the media would have us believe. But are all of these things really true? - math that mattersLet’s investigate!YearAverage counts of young persons in Canadian provincial and territorial correctional services (ie. kids in jail)19972020.419982012.619991830.22000185120011760.420021630.320031008.62004962.92005841.62006775.22007800.82008696.12009683.6498157592710Starting/Main screen00Starting/Main screen***If you ever get stuck on a menu, try pressing “esc”.IF you turn on the calculator and you don’t see the main screen, press the red “X” in the top right hand corner to close the page. When it asks if you want to save the file, click “No”.5048250185420Touch pad00Touch padPart1: Create a new “Document”Press “1” on the main screen to get a New Document or scroll to New Document with the touchpad.Part 2: Enter the table of values into the Calculator501015027622500Press “4” to select Add Lists & Spreadsheet or scroll to it using the touch pad and click.Starting with column “A”, press up on the touch pad twice to highlight the box containing “A”. This box is above the bluish/gray line. Type “x” into the box.Press right on the touch pad to get to the box containing “B”. Type “y” into the box.4895850-7112000Enter your points into the appropriate columns and rows, moving between boxes using the touch pad. Do Not Type Anything in the Bluish/Gray Line! (See the picture on the right)After you have typed in your last value from the table, press “enter”.Part 3: Display the Scatter Plot48958501460500Press “ctrl” “doc” to select + page. Select 5: Add Data & Statistics.You should now see the words “Click to add variable” on the bottom of the screen and on the left side of the screen.489585026987500On the bottom of the screen, click on the words “Click to add variable”. Select x.On the left side of the screen, there are no words, but you can click the middle area (where “Click to add variable” was in step 3. Select y. You should now see the scatterplot.Describe the trends. Describe the relationship between the year and the average count of young persons in correctional facilities.4476750196850025615901905000Part 4: Add a Line of Best fitPress “menu”.Press “4” to get Analyze.Press “6” to get Regression.Press “1” to get Show Linear (mx+b) You should now see a line on your screen.What is the equation of your line of best fit? ____________________Part 5: Set up Go back to the tab “1.1” in the top left corner of the screen.Press Menu 4:Statistics 1: Stat Calculations 3:Linear Regression (mx+b)In the “X List” box, press “x”.In the “Y List” box, press “y”.Press “Ok” If it asks whether you want a column reference or variable reference, choose variable reference, then press OK. Do this for both x and y.Press “ctrl” “doc” to select + page.Press “1” to Add Calculator.Part 6: Interpolate/Extrapolate To interpolate or extrapolate, press “var”. Select “f1” from the list and press enter.“f1()” should appear on the screen. Enter the x-value (year) that you are trying to interpolate/extrapolate. For example, if you want to find the average count of youths in a correctional facility in the year 1995, you would see “f1(1995)” on the screen.Press “enter”. The value you want should be on the right side of the screen.Estimate the average count of youths in a correctional facility in the year 1995.Estimate: _________Is this interpolation or extrapolation? _______________Estimate the average count of youths in a correctional facility in the year 2012.Estimate: _________Is this interpolation or extrapolation? _______________Estimate the average count of youths in a correctional facility in the year 2015.Estimate: _________Is this interpolation or extrapolation? _______________Does this answer make sense? ___________________Predictions can be very inaccurate if you try to extrapolate too far from the data set, particularly if you are not sure that your line or curve of best fit accurately fits the trend. Part 7: To shut down calculatorClick the red “X” in the top right corner of the screen.When it asks if you want to save the file, click “No”.To shut down, press “ctrl” “on” to select off.A study of 800 Canadian newspapers found interesting patterns. Although violent crime accounts for approximately 11% of all crime in Canada, a full 25% of criminal justice stories had to do with homicide, and more than 50% contained elements of violence. Three major papers in Toronto found that 94% of crime stories about youth were about violent offences compared to the less than 25% of Ontario youth cases involving violence. When questioned, editors acknowledged that they “typically only report the worst types of crime and the worst cases of those crimes” (John Howard Society of Alberta, 1998. “Youth Crime in Canada. Public Perception vs. Statistical Information”Why do you think that papers report the worst cases of the worst types of crimes?Homework: pg. 85 #5, 6, 7 Extension #11, 12, 13 ................
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