ESSENTIAL QUESTION: HOW CAN WE USE MATH TO PREDICT THE FUTURE? 7.1 Fitting Data to a Line.
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Post on 01-Jan-2016
7.1 Fitting Data to a LineEssential Question: How can we use math to predict the future? 7.1 Fitting Data to a LineFitting a Line to DataThis is called three different things: Least Squares RegressionLinear RegressionBest Fit LineIt involves estimating a line of fit for a scatter plot then finding the slope and y-intercept of the dataYou can then plug in any x value to get a corresponding y-value potentially predicting future data values that have not happened yetPositive Slope/Pts are close togetherNegative Slope/Pts are close togetherTypes of Correlation:Correlation is how closely the line matches the data (pts close together = good; pts spread out =bad) No Correlation can't really tell if it is positive or negativeYou cannot really draw a line that would fit all the dataThe data has a really bad r-value and potentially high standard deviation for "y" or output values Types of Correlation ContinuedHow do we use the calculator to find the best fit line/linear regression line/least square regression line? Plug the data into your lists: Press Stat then Edit to go to the listsMake sure it is referencing L1 and L2Enter data in each list (when putting in yearly data always refer to the starting point as year zero)After all data is entered: Press Stat Right 4-Enter to find the LinReg linea is the slopeb is the y-intYou can plug in future values to find future data pointsWhat does least square regression mean? AppletMedian Median LineFind the mean, median, and std. dev for each data set below: A) 1,5,7,486B) 1,5,7,12Which data measure is unaffected by the outlier? This is a line of best fit that is not influenced by outliers similar to the way the median is not influenced by outliers in the data. Which of the below would be the Median-Median line of the data red or green? Correlation and CausationAn R-Value above 0.7 is a good positive correlationAn R-Value below -0.7 is a good negative correlationA good correlation does not necessarily imply a causation. Examples: Hours of study correlated with test gradesLower likelihood of cancer due to taking a certain pharmaceuticalWhen Michael Turner rushes more than 20 times the Falcons are 15-1 etc. Correlation means there is a good mathematical relationship, so we can use it to predict future values. Causation means that x caused y or vice versa this is rarely true. When given a scenario you can almost always argue there is no causationThere are times you can argue that a cause and effect relationship exists between the independent and dependant variables if you have a good reason the answer could be accepted. HIGH Q!Types of SamplesSimple Random Sample (SRS) best type of sample, each data point has an equal opportunity of being chosenSelf Selected Sample those in the population who chose to volunteer data are in the sample. Convenience Sample those in the population who are easiest to reach are in the sample. Systematic Sample a rule is used to sample, every fourth person is chosen, every other data point is chosen etc. (this is probably the second best of these options)BiasHow do we determine bias in a sample? If a sample is biased it means that certain parts of the population are underrepresented. Examples: Only sampling college students. Internet surveys. Measuring the average height and weight of American Males and declaring this is the average height and weight of humans.
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