Analyzing Least-Squares RegressionIntroduction:This project will display three data sets that were created by Frank Ascombe to show what happens when calculating before or without plotting the data first. All three sets have the same correlation and the same least-squares regression line to several decimal places.Analysis: I first created a scatter plot for each data set and followed the general guidelines to create a perfect scatter plot. Scatter plots show how much one variable is affected by another. I then used the correlationequation (y=a+bx) to understand the relations between the data sets. However, all data sets had a correlation coefficient of ether exact or about.82 therefore their relationships were moderate. I categorized them as moderate because we were given a general guideline to the categories and .82 happens to fall in the “moderate” category. Data Set A: y=a+bx a=2.96 b=.51y=2.96x+.51 r=.82moderate correlational relationship Date Set B: y=a+bx a=3.00 b=.50 y=3x+.5 r=.816moderate correlation relationshipData Set C:y=a+bx a=.50b=3.0 y=.50+3.0xr= about .moderate correlation relationship 3.) In date set C, all variables in the X variable set were 8 except one which was 16 which proved to be an obvious outlier on the X axis. However, that same point was also an obvious outlier on the Y axis. 4.) Both sets A and B have “r” values above .80. This indicates that they both have moderately strong linear relations, which in return means that that the data points are falling close to the line of best fit. You are able to use the line of best fit to estimate the value of y since you are given x. Part C cannot use the line of best fit to estimate y because the data points are scattered therefore you can’t use the line to accurately make a prediction.Conclusion:Frank Anscombe’s illustration did a fantastic job of proving his point (plot before calculating) to be true. Almost all data was very consistent with the exception of one outlier in Data Set C. This is a very useful lesson to apply for future
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