Question

Ten corvettes between 1 and 6 years old were randomly selected from the classified ads of The Arizona Republic. The following data were obtained, where x denotes age, in years, and y denotes price, in hundreds of dollars.

X: 6 6 6 2 2 5 4 5 1 4

Y: 270 260 275 405 364 295 335 308 405 305

(A) Draw a scatter diagram

(B) Find the Linear Correlation coefficient r.

(C) Describe the shape, strength, and direction.

(D) Does a linear relationship exist

(E) between the age of a corvette and its price? (use the critical value to explain)

(F) If appropriate, explain the slope in context.

(G) If appropriate, explain the y-intercept in context.

(H) Predict the price of a one-year-old corvette.

(I) Find the Residual of a one-year-old corvette.

Answer 1

X	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
6 6 6 2 2 5 4 5 1 4	270 260 275 405 364 295 335 308 405 305	3.610 3.610 3.610 4.410 4.410 0.810 0.010 0.810 9.610 0.010 Sum: 30.900	2724.840 3868.840 2227.840 6855.840 1747.240 739.840 163.840 201.640 6855.840 295.840 Sum: 25681.600	-99.180 -118.180 -89.680 -173.880 -87.780 -24.480 -1.280 -12.780 -256.680 1.720 Sum: -​​​​​​862.200