Linear and Quadratic Regression

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Curve Fitting: Linear or Quadratic? Ellen and Kelly test Ellen’s new car in an empty parking lot. They mark a braking line where Ellen applies the brakes. Kelly them measures the distance from that line to the place where Ellen stops. Below is the relationship of their speed and stopping distance. Speed (mi/h) | 5 | 10 | 15 | 20 | 25 | Stopping Distance (ft) | 7 | 17 | 30 | 46 | 65 | A linear regression shows the relation in a scatter plot of data. The regression is represented by a straight line entered to the graph to show how strong the correlation is. A quadratic regression is a parabola that shows the relation between data on a scatter plot, to show how strong the correlation is. To find out whether a linear regression or a quadratic regression organized the data more accurately I calculated each regression on my calculator and looked at which correlation coefficient was stronger. To find the linear regression I used my calculator and went to stat and typed in the data then went to ”Stat – Calc - LinReg(ax+b) – Calc”. It gave me the formula for the data on the scatter plot. Y = 2.9x + 10.5 and the correlation coefficient is .9925. This means the correlation is very strong since it is close to 1. The closer the correlation coefficient is to 1 or -1 the stronger it is. To find the quadratic regression I went to “Stat – Calc – QuadReg – Calc”. The formula was y = .06x + 1.1 and the correlation coefficient was 1. This means the quadratic regression fits the data perfectly. Using the information that I gathered between the two regressions, quadratic regression is the best answer. (EXCEL) An example of a job or career that requires linear and quadratic regressions is an Actuary. They use data to predict trends for insurance companies. Such as how long people born in a certain year, or in a particular region, would be expected to live, or how many

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