Statistics: Correlation and Regression
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Let x be the age of licensed driver in years. Let y be the percentage of all fatal accidents(for a given age)due to failure to yield the right of way. For example, the first data pair says that 5% pof all fatal accidents involving 37year olds are due to failure to yield the right of way.
X: 37, 47, 57, 67, 77, 87
Y: 5, 8, 10 , 16, 30, 43
Complete parts a) to e) given Ex= 372, Ey = 112, Ex^2 = 24,814, Ey^2 = 3194, and Exy=8254, and r= 0.943
a) Draw a scatter gram display the data
b) Verify the sums: Ex, Ey, Ex^2, Ey^2,and the value of the sample correlation coefficient r.
c) Find x( line over x) and y(line over the y) and a and b. Then find the equation of the least squared line y( with this^ over the y)=a+bx.
d) Gragh the least squares line on your scatter diagram. Be sure to use the point (x,y, both with lines over each one) as one of the points on the line.
e) Find the value of the coefficient determination r^2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? what percentage is unexplained?
f) Predict the percentage of all fatal accidents due to failing to yield the right of way for 70 year olds.
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