Aa Aa E. 2. Properties of the least squares line #2 In the United States, tire t

Question

Aa Aa E. 2. Properties of the least squares line #2 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: Tread Depth Mileage Tire (10,000 miles) (32nds of an inch) Think about the population of tires. Each tire in the population has a value of x (its mileage) and a corresponding value of y (its tread depth). If the relationship between x and y is linear, the equation that describes how y is related to x and an error term is: You can use sample data to estimate the parameters Bo and B1 and obtain the following estimated regression equation, where y is the predicted value of y: bo b1x The difference between y and y for a particular data point (observation) is called a residual. The formula for the slope of the least-squares line is provided as follows. Enter the values for the numerator and denominator, and then enter the value of b1. Exi2 (2x)2 n

Explanation / Answer

b1 = 4 * 55 - 10* 24 / [4* 30- 10*10] = -1

Sample mean for mileage x_bar = (1+2+3+4)/4=2.5

Sample mean for thread depth = [8+6+5+5]/4=24/4=6

y-intercept of least squares line is given by (24*30-10*55)/(4*30-10*10)=8.5

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.