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 ReasoningFirst Year Program requirementPrereq to course is ISP 110 or Math 101 or placement through advisingKnow 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 itTo graph and manipulate we will use mathematics and technologyWhy 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 coursesIn your job – career advancementsIn 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 modelsUseful percentagesGraphingConsumer Price IndexAbsolute versus relative valuesFinancial modelsWhat is LSP 120?Let’s take a closer look at the syllabusLSP 120Linear Modelsand TrendlinesLinear RelationshipsWhat 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, orThe change in y per unit change in x is constant, orThere is a constant rate of changeLinear RelationshipsWhy 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 futureWe can also go back in time and see where the data has been!Linear RelationshipsLook 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 RelationshipsIf it is linear, what is the function?Recall: y = mx + bm is the slope, or the (change in y) / (change in x)b is the y interceptSo calculate the slopeThen 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 RelationshipsLinear growth – occurs when a quantity grows by the same absolute amountExponential growth – occurs when a quantity grows by the same relative amount – that is by the same percentage – in each unit of timeThere is also linear decay and exponential decayExamplesThe 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.TrendlinesReal data is seldom perfectly linearSuppose 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.TrendlinesIf 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?TrendlinesDo we have to do this calculation?No, Excel can do it for youLet’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 boxesTrendlinesLet’s take a look at the dataset Motorcycles_By_Year2005.xlsGraph the data using an XY Scatter. After the graph is done, right click on a data point, select Add TrendlineTrendlinesHow 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!!TrendlinesYou can use the equation for the trendline, but the terms in the trendline equation are significantly rounded.Can remove some of this roundingRight-click on the formula in the graph and then click on Format Trendline LabelSelect Number on left and rightLet’s give it 6 decimal placesTrendlinesYou can also have Excel calculate the Slope and Intercept individually, and then use them in an equationSomewhere 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 ActivityBut first, let’s break up into