In the United States, tire tread depth is measured in 32nds of an inch. Car tires typically start out with 10/32 to 11/3

Post by **answerhappygod** » Wed May 11, 2022 4:01 pm

: In The United States Tire Tread Depth Is Measured In 32nds Of An Inch Car Tires Typically Start Out With 10 32 To 11 3 1 (32.18 KiB) Viewed 21 times

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 Tire (10,000 miles) Tread Depth (32nds of an inch) 8 1 1 2 2 8 3 3 7 4 4 5 A scatter diagram of the sample data is shown below (blue points). The line y = 11 - 2x is also shown in orange. ? 10 A o 0 Sum of Distances O + o (x-bar, y-bar) TRE AD DEPTH (32nds of an) 0 MILEAGE (10,000 miles)

Now 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: y = Bo + Bix + c You can use sample data to estimate the parameters Bo and B1 and obtain the following estimated regression equation, where ŷ is the predicted value of y: ý = b + 1x The difference between y and y for a particular sample point (observation) is called a residual. Suppose you fit a least squares regression line to the four sample points on the graph. Based on your work so far, even before you fit the line, you know that the sum of the residuals is . In addition, being as specific as you can be, you know that the sum of the squared residuals is An alternate formula for the slope of the least squares line is provided below. Enter the values for the numerator and denominator, and then enter the value of bl. bi Y($i) - (vi)/- X-(x/n The y intercept of the least squares regression line is On the below scatter diagram of the sample points, use the orange line (square symbols) to plot the least squares regression line, then use the olive line (dash symbols) to plot the y = y line. There are three sums of squares that are foundational to regression analysis: the SST (total sum of the squares), SSR (sum of squares due to regression), and SSE (sum of squares due to error). Regardless of the sum of squares, for each observation, a particular distance is measured and squared, and then the squares are summed. Consider tire 4. Use the green points (triangle symbol) to mark the distance for tire 4 that is squared and included in the SSR. Then use the purple points (diamond symbol) to mark the distance for tire 4 that is squared and included in the SSE. Line segments will automatically connect the points. 4

Now 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: y = Bo + Bix + c You can use sample data to estimate the parameters Bo and B1 and obtain the following estimated regression equation, where ŷ is the predicted value of y: ý = b + 1x The difference between y and y for a particular sample point (observation) is called a residual. Suppose you fit a least squares regression line to the four sample points on the graph. Based on your work so far, even before you fit the line, you know that the sum of the residuals is . In addition, being as specific as you can be, you know that the sum of the squared residuals is An alternate formula for the slope of the least squares line is provided below. Enter the values for the numerator and denominator, and then enter the value of bl. bi Y($i) - (vi)/- X-(x/n The y intercept of the least squares regression line is On the below scatter diagram of the sample points, use the orange line (square symbols) to plot the least squares regression line, then use the olive line (dash symbols) to plot the y = y line. There are three sums of squares that are foundational to regression analysis: the SST (total sum of the squares), SSR (sum of squares due to regression), and SSE (sum of squares due to error). Regardless of the sum of squares, for each observation, a particular distance is measured and squared, and then the squares are summed. Consider tire 4. Use the green points (triangle symbol) to mark the distance for tire 4 that is squared and included in the SSR. Then use the purple points (diamond symbol) to mark the distance for tire 4 that is squared and included in the SSE. Line segments will automatically connect the points. 4

On the below scatter diagram of the sample points, use the orange line (square symbols) to plot the least squares regression line, then use the olive line (dash symbols) to plot the y = ý line. There are three sums of squares that are foundational to regression analysis: the SST (total sum of the squares), SSR (sum of squares due to regression), and SSE (sum of squares due to error). Regardless of the sum of squares, for each observation, a particular distance is measured and squared, and then the squares are summed. Consider tire 4. Use the green points (triangle symbol) to mark the distance for tire 4 that is squared and included in the SSR. Then use the purple points (diamond symbol) to mark the distance for tire 4 that is squared and included in the SSE. Line segments will automatically connect the points. 10 9 8 O Least Squares Lines O o 6 SSR Building Block TREAD DEPTH (32nds of an inch) 5 o SSE Building Block 2 y = y-bar 1 0 4 2 3 TIRE MILEAGE (10,000 miles) The value of the SSE is