Welcome to LSP 120What is LSP 120?Slide 3Slide 4Slide 5Slide 6What are the topics?Slide 8LSP 120Linear RelationshipsSlide 11Slide 12Slide 13Slide 14ExamplesSlide 16Slide 17TrendlinesSlide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Let’s Go!Welcome to LSP 120Dr. Curt M. WhiteWhat is LSP 120?First course in QRTL (Quantitative Reasoning and Technological Literacy)Also known as Quantitative ReasoningFirst Year Program requirementPrereq to course is ISP 110 or Math 101 or placement through advisingKnow this stuff already? Take the exam this week.What is LSP 120?We will examine data – look at it, talk about it, graph it, manipulate itTo graph and manipulate we will use mathematics and technologyWhy do we want to do this?What is LSP 120?Because the person that can use data (information) gains knowledge and thus has power!In college – writing research papers and taking advanced coursesIn your job – career advancementsIn government – getting things done (?)In life – more intelligent life decisionsWhat is LSP 120?“Information is a beacon, a cudgel, an olive branch, a deterrent – all depending on who wields it and how. Information is so powerful that the assumption of information, even if the information does not actually exist, can have a sobering effect.”What are the topics?Linear and near-linear models (with trendlines and forecasting)Exponential modelsUseful percentagesGraphingConsumer Price IndexAbsolute versus relative valuesFinancial modelsWhat is LSP 120?Let’s take a closer look at the syllabusLSP 120Linear Modelsand TrendlinesLinear RelationshipsWhat makes a graph or function or table of values linear? (You have already seen this!)For a fixed change in x, there is a fixed change in y, orThe change in y per unit change in x is constant, orThere is a constant rate of changeLinear RelationshipsWhy do we care if a set of data is linear?If a data set is linear (or near-linear), then we can better predict where the data will be in the futureWe can also go back in time and see where the data has been!Linear RelationshipsLook at a set of values. Is it a linear relationship? Apply (B3-B2)/(A3-A2)2 4 253 5 504 6 755 7 1006 8 1257 9 150No entry in this first row=(B3-B2)/(A3-A2) = (50-25)/(5-4) = 25=(B4-B3)/(A4-A3) = (75-50)/(6-5) = 25=(B5-B4)/(A5-A4) = (100-75)/(7-6) = 25=(B6-B5)/(A6-A5) = (125-100)/(8-7) = 25=(B7-B6)/(A7-A6) = (150-125)/(9-8) = 25 Column A Column B (X values) (Y values) All the results are the same (25), so this is a linear set of values.Linear RelationshipsIf it is linear, what is the function?Recall: y = mx + bm is the slope, or the (change in y) / (change in x)b is the y interceptSo calculate the slopeThen plug in slope and first x and y values into y=mx+b and solve for bLinear Relationships2 4 253 5 504 6 755 7 1006 8 1257 9 150No calculation in this row(B3-B2)/(A3-A2) = (50-25)/(5-4) = 25(B4-B3)/(A4-A3) = (75-50)/(6-5) = 25(B5-B4)/(A5-A4) = (100-75)/(7-6) = 25(B6-B5)/(A6-A5) = (125-100)/(8-7) = 25(B7-B6)/(A7-A6) = (150-125)/(9-8) = 25 A(or X) B(or Y)y = mx + bm = change in y / change in x = 25/1 = 2525 = 25 * 4 + bb = -75 (this is the y-intercept)y = 25x – 75 This is the equation of the lineExamplesx y5 -410 -115 220 5x y0 12 44 166 36x y3 54 96 119 17x y Rate of Change3 56 9 =(B3-B2)/(A3-A2)9 1312 17m=change y / change x = 3/5=0.6y = mx+b -4=0.6*5+b b=-7y = 0.6x - 7Linear RelationshipsLinear growth – occurs when a quantity grows by the same absolute amountExponential growth – occurs when a quantity grows by the same relative amount – that is by the same percentage – in each unit of timeThere is also linear decay and exponential decayExamplesThe number of students at Wilson High School has increased by 50 in each of the past four years.The price of milk has been rising with inflation at 3% per year.Tax law allows you to depreciate the value of your equipment by $200 per year.The memory capacity of computer hard drives is doubling approximately every two years.The price of DVDs has been falling by about 25% per year.TrendlinesReal data is seldom perfectly linearSuppose the data is reasonably linear or near-linear? How does one make a linear model of the data?The standard approach is to use a “best-fit” lineIn Excel – note the equation for the trendline and the R2 value.TrendlinesIf R2 = 1, then 100% of the variance in y is explained by the line, so we have a perfect fit (the data is linear)If R2 = 0, then we have a terrible fit. (Better not make a prediction)What if R2 value = 0.5?TrendlinesDo we have to do this calculation?No, Excel can do it for youLet’s say you have made a graph of some data using ExcelAfter you make a graph, right-click on any datapoint.Select Add Trendline…Then check the two bottom boxesTrendlinesLet’s take a look at the dataset Motorcycles_By_Year2005.xlsGraph the data using an XY Scatter. After the graph is done, right click on a data point, select Add TrendlineTrendlinesHow do you make a prediction?Two possible techniques: 1. Extend the trendline using Excel 2. Use the slope / intercept model (next slide)Be careful! One’s confidence in predictions made far from the data must be tempered!!TrendlinesYou can use the equation for the trendline, but the terms in the trendline equation are significantly rounded.Can remove some of this roundingRight-click on the formula in the graph and then click on Format Trendline LabelSelect Number on left and rightLet’s give it 6 decimal placesTrendlinesYou can also have Excel calculate the Slope and Intercept individually, and then use them in an equationSomewhere in Excel, enter label Slope and in next cell to right, enter =Slope(Do the same thing for InterceptLet’s Go!Let’s head to the lab and start our first ActivityBut first, let’s break up into
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