Question

In the United States, tire tread depth is measured in 32nds of an inch. Car tires typically start out with 10/32 to 11/32 of an inch of tread depth. In most states, a tire is legally worn out when its tread depth reaches 2/32 of an inch. A random sample of four tires provides the following data on mileage and tread depth: Mileage (10,000 miles) Tread Depth (32nds of an inch) Tire You vwill use the sample data to find the equation of the least-squares regression line. The formula for the slope of the least-squares regression line is provided here. Enter the values for the numerator and denominator, and then enter the value of b. nžx2-(2x)2 The sample mean for mileage is (32nds of an inch). Hence, the y-intercept of the least-squares regression I (10,000 miles), and the sample mean 9 for tread depth is line is (32nds of an inch). On the following scatter diagram, use the orange line (square symbols) to plot the least-squares regression line. TREAD DEPTH 132nds of an inch 10 Least-Squares Lin Prediction TIRE MILEAGE İ 10,000 miles! he เป įamar Use the black X to mark the point that corresponds to the predicted tread depth for a tire with mileage x-35,000 miles. The predicted tread depth for a tire that has been driven 35,000 miles is (32nds of an inch) and the standard deviation of tread depth is ,- The standard deviation of mileage is s Therefore, the sample correlation coefficient is of the variation in tread depth can be explained by the vanation in mileage and the least-squares of the variation in tread depth is due to random chance or the possibility of lrking About regression line. About veriables that influence tread depth.

Answer 1

we have - 6 2S 2.O 5S30 ISo estimated eq uation aLx where

2 6

2 叉

N ow 2.S)+C2-2-S) C3- 2.S 2 2. S 41

1.41421 Cov(X4

Cov(X) 191 1414214) = -0.9128 128) o.8 333

in mileage and fhe leat sqares vegressior thal (nflence tread durth