1. Properties of the least squares line #1 Aa Aa In the United States, tire trea

Question

1. Properties of the least squares line #1 Aa Aa 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 Tread Depth Tire (10,000 miles) (32nds of an inch) A scatter diagram of the sample data follows (blue points). The line y 11 2x is shown in orange.

Explanation / Answer

1) Y = 11 - 2x gives slope = -2

Mean_X = (1+2+3+4)/4 = 2.5

Mean_Y = (8+8+7+5)/4 = 7

Mean = (2.5, 7)

line passing through Mean (2.5, 7) with slope -2

y = -2x +c

7 = -2*(2.5) + c

c = 7 + 5 = 12

y = 12 - 2x

2) Sum of residual

y = 11 -2x

x = 1: y = 9 residual = 8 -9 = -1

x = 2: y = 7 residual = 8 - 7 = 1

x = 3: y = 5 residual = 7 - 5 = 2

x = 4: y = 3 residual = 5 - 3 = 2

sum of residual = -1 + 1 + 2 + 2 = 4

3) Sum of suared residual = 1 + 1 + 4 + 4 = 10

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