1. First-order linear model Aa Aa In the United States, tire tread depth is meas
ID: 3365523 • Letter: 1
Question
1. First-order linear model 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) 2 2 4 4 4 A scatter diagram of the sample data follows [blue points (circle symbols): The line y = 8-x is also shown in orange TREAD DEPTH (32nds of an inchl 0 Sum of Distances (x-bar, y-bar) MILEAGE (10,000 miles] Clear All Think about how close the line y 8-x is to the sample points. Look at the graph, and find each point's vertical distance from the line. If the point sits above the line, the distance is positive; if the point sits below the line, the distance is negative. The sum of the vertical distances between the sample points and the orange line is 4 and the sum of the squared vertical distances between the sample points and the line isExplanation / Answer
The sum of squared vertical distances between the sample points and the line is 10
The line you plotted passing through the point (xbar, ybar)
The sum of squared vertical distances between the sample points and the line that you just plotted is 0.25^2+0.25^2+0.25^2+0.25^2=0.25
Correct Answer: Option (C) the line you plotted that has a sum of the distances equatl to zero
The sum of the residuals is zero
The sum of the squared residuals is minimum
From the given data
b1 =[ 35 - (10*18)/4 ] / [35 - 10^2 / 4] = -10 / 5 = -2
Y-intercept of the least square line is 9.50
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