Question

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 34% of all fatal accidents of 17-year-olds are due to speeding. x 17 27 37 47 57 67 77 y 34 22 22 12 10 7 5 Complete parts (a) through (e), given Σx = 329, Σy = 112, Σx2 = 18,263, Σy2 = 2442, Σxy = 3974, and r ≈ −0.956. (a) Draw a scatter diagram displaying the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 5101520253035404550556065707580510152025303540 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. (b) 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 = (c) 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 (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (e) 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 35-year-olds. (Round your answer to two decimal places.) % Need Help?

Answer 1

Part a)

Part b)

	X	Y	X * Y	X2	Y2
	17	34	578	289	1156
	27	22	594	729	484
	37	22	814	1369	484
	47	12	564	2209	144
	57	10	570	3249	100
	67	7	469	4489	49
	77	5	385	5929	25
Total	329	112	3974	18263	2442

r = -0.956

Part c)

X̅ = Σ( Xi / n ) = 329/7 = 47
Y̅ = Σ( Yi / n ) = 112/7 = 16

Equation of regression line is Ŷ = a + bX


b = -0.461
a =( Σ Y - ( b * Σ X) ) / n
a =( 112 - ( -0.4607 * 329 ) ) / 7
a = 37.654
Equation of regression line becomes Ŷ = 37.654 - 0.461 X

Part e)

Coefficient of Determination
R² = r² = 0.914
Explained variation = 0.914* 100 = 91.4%
Unexplained variation = 1 - 0.914* 100 = 8.6%

Part f)

When X = 35
Ŷ = 37.654 + -0.461 X
Ŷ = 37.654 + ( -0.461 * 35 )
Ŷ = 21.52