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Value of the sample correlation coefficient

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Reference no: EM131954436

Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 35% of all fatal accidents of 17-year-olds are due to speeding.

x 17 27 37 47 57 67 77

y 35 24 19 12 10 7 5

given: 

Σx = 329, Σy = 112, Σx2 = 18,263, Σy2 = 2480, Σxy = 3934, and r ≈ -0.958.

(a) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx =  

Σy =  

Σx2 =  

Σy2 =  

Σxy =  

r =  

(b) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x =  

y =  

y hat =  ______+  ______x

(c) Find the value of the coefficient of determination r2. 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? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =  

explained _______%

unexplained_______%

(f) Predict the percentage of all fatal accidents due to speeding for 20-year-olds. (Round your answer to two decimal places.)

 _______%

Reference no: EM131954436

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