Correlation and Regression

Correlation and Regression

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  • We are going to use the Desmos calculator to identify the correlation and regression properties. 
  • The data set for bivariate data which comparing two variables, The grades versus how much studying hours the students do in a day.
  • The data points are 55, 32, 67, 100, 98, 75, 46, 82, 72, 93, 44, 26, 67 for 13 days. The graph has an outlier that is an influential point to change the regression line. The dots or data on the graph have a bad correlation.
  • The data points for the independent variables or the predictor variables is the hours studying and the dependent variables or the response variables is the grades the students get.  
  • First, we will try the exponential recursive formula of y= a*b^x. I got the regression equation of y= 303.77*1.02^x.The residual of the data is 0.779 and forms a residual plot. It makes a regression line that is not that far from 0. The mathematical model made from the equation could be better.
  • The cluster on one part of dots make it a bad correlation. We will use a transformation to fix it to a good correlation.  
  • We can't use the  least-squares property that is the same as a regression this is because we have an outlier. 
  • That equation was for a data set with exponential growth and decay. We made our first nonlinear transformation now we should try to see which one is closer to 1. 
  • The power transformation is 305.08*x^.04 and the residual is 0.887. The relationship between the response and the predictors is not linear.  A linear transformation's residual is 0.622.
  • Least absolute deviation is less easy to work with mathematically. The regression will be stronger, but it has more than one best-fitting line.  
  • The logarithmic transformation is for if the correlation is high end and highly skewed.  It is easy to use and will make the correlation more normal distribution.  The residual values have not been high like 24 so this method is not needed.
  • The last transformation we will do is the median-median line. This method divides the data into sets, then finds the median. Next it finds the slope and y-intercept. The regression equation is 5x+302.8 and has a residual of 0.876. The marginal change is the amount the variable x changes by one unit that is represented by y. 
  • The power transformation is the linear correlation coefficient becuase the residual is the farthest from zero. 
  • I want to go over iteration, this is the repetition of a process in order to generate a sequence of outcomes. The outcome of each iteration is then the starting point of the next iteration. So solve for 6,9,12,15. 3-x+5
  • The first number would be 3 so 3-2+5= 9 ,-2+5=12, then -2+5= 15
  • We went over everything that deals with calculating errors in statistics. Compound interest is used in statistics to save money. 
  • An investment earns 3% compounded monthly. Find the value of an initial investment of $5,000 after 6 years. A= P(1+r/n)^nt A=amount, p= initial, 5000, r=interest rate, 0.03, m=12 since monthy 1 if yearly, t=years, 6. 
  • After 6 years it would be $5,984.74.
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