Please help explain the question, working out, below

ng.cengage.com/static b/u i/evo/i ndex.html?deploymentld= 5991112234171050575852888863681el5 B N = 9780170389723&id=1121159432... 1} Q if CENGAGE I MINDTAP Q Search this course 0 ; Ruby v MindTap Week 12 [Revision] X 4. Measures of linear relationship Least squares rnelhod and the coefcient of determination Consider a data set consisting of values for three variables: X, Y, and Z. Their sample means, standard deviations, and correlations (with Y) are: Sample Mean )2 = 3.4 f = 26.21 i = 6.68 Sample Standard Deviation s, = 2.29 sy = 7.12 s, = 1.5 Sample Correlation (with Y) 1'13. = 0.89 I\" = 1 1'5, = 0.14 Consider the least squares line 9 = b0 + tax. The slope of this least squares line is V , and the intercept is V . The variation in the variable X explains V of the variation in the variable Y. Consider the least squares line 9 = on + clz. The slope of this least squares line is V , and the intercept is V . The variation in the variable Z explains V of the variation in the variable Y. Scatter Diagram A ,0 Type here to search MindTap Week 12 [Revision] X MindTap - Cengage Learning X Data Assignment 2.docx X + X C ng.cengage.com/staticb/ui/evo/index.html?deploymentld=59911122341710505758528888636&elSBN=9780170389723&id=1121159432... P Update Apps M Uni M Inbox & My Uni Access Adelaide -... Criminal Law Data Analytics Com T Uni Important Law Finished Course Hero "> Reading list CENGAGE | MINDTAP Q Search this course ? Ruby v MindTap Week 12 [Revision] X 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) 1 1 8 A-Z 2 CO W N W A 4 6 A scatter diagram of the sample data follows [blue points (circle symbols)]. The line y = 11 - 2x is also shown in orange. 10 Type here to search O E w 6:10 PM 01:56 ENG 6/06/2021MindTap Week 12 [Revision] X MindTap - Cengage Learning X Data Assignment 2.docx X + X C ng.cengage.com/staticb/ui/evo/index.html?deploymentld=59911122341710505758528888636&elSBN=9780170389723&id=1121159432... P Update Apps M Uni Mi Inbox & My Uni Access Adelaide -... Criminal Law Data Analytics . Com T Uni Important Law Finished Course Hero "> Reading list CENGAGE | MINDTAP Q Search this course ? Ruby v MindTap Week 12 [Revision] X A scatter diagram of the sample data follows [blue points (circle symbols)]. The line y = 11 - 2x is also shown in orange. 10 A 8 O O 0 Sum of Distances A-Z O 6 (x-bar, y-bar) TREAD DEPTH (32nds of an inch) O 6 2 2 3 4 5 MILEAGE (10,000 miles) Type here to search O w 6:10 PM 01:56 ENG 6/06/2021 a? MindTiP 7 Cengage Learning X ( 9 0' i ng.cengagecom/staticb/ui/evo/index.html?deploymentld=599111223417105057585288886368eISBN=978017038972381id=1121159432... i} E *- EJ- e Apps M Uni M Inbox Q My Uni e AccessAdelaide .___ I n Criminal Law l " DataAnalytitS l n ComT l n Uni Important l " Law l n Finished u Course Hero I l Reading list '3' CENGAGE I MINDTAP Q Search this course 0 ; Ruby v MindTap Week 12 [Revision] Think about how close the line y = 11 - Ex is to the sample points. Look at the graph, and nd 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 V , and the sum of the squared vertical distances between the sample poinls and the line is V . 0n the graph, use the green line (triangle symbols) to plot the line that has the same slope as the line y = 11 2x, but with the additional property that the vertical distances between the points and the line sum to 0. Then place the black point (X symbol) on the graph to plot the point (i, y) where i is the mean mileage for the four tires in the sample and )7 is the mean tread depth for the four tires in the sample. The line you just plotted V through the point (3;, fr). The sum of the squared vertical distances between the sample points and the line that you just plotted is V . According to the criterion used in the least squares method, which of the two lines provides a better fit to the data? 0 y = 11 2x 0 Neitherthe two lines t the data equally well 0 The line you plotted that has a sum of the distances equal to 0 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 relationshi between x and is linear the e uation that describes how y is related to x and some error variable is: 6:10 PM D A I) a) E \"f ENG 6/06/2021 E I i a) a. ,0 Type here to search 0 ll ng.cengage.com/static b/u i/evo/i ndex.html?deploymentld= 5991112234171050575852888863681el5 B N = 9780170389723&id=1121159432... 1} Q I 'I.' CENGAGE I MINDTAP Q Search this course 0 ; Ruby v MindTap Week 12 [Revision] X Now think about the population of tires. Each tire in the population has a value of x (its mileage) and a corresponding value ofy (its tread depth). If ' the relationship between x and y is linear, the equation that describes how y is related to x and some error variable is: y=Bu+le+e You can use the sample data to estimate the parameters Sn and BI and obtain the following estimated regression equation, where f is the predicted value of y: fz=bu+b1x The difference between V and j} for a particular sample point (observation) is called a residual. Suppose you use the least squares method to nd the least squares line for the four sample points on the graph. 0n the basis of your work so far, even before you t the line, you know that the sum of the residuals is V . In addition, you know that the sum of the squared residuals is V . ,0 Type here to search MindTap Week 12 [Revision] X MindTap - Cengage Learning X Data Assignment 2.docx X + X C ng.cengage.com/staticb/ui/evo/index.html?deploymentld=59911122341710505758528888636&elSBN=9780170389723&id=1121159432... P Update Apps M Uni M Inbox My Uni Access Adelaide -... Criminal Law Data Analytics . Com T Uni Important Law Finished Course Hero "> Reading list CENGAGE |MINDTAP Q Search this course ? Ruby v MindTap Week 12 [Revision] X An alternate formula for the slope of the least squares line follows. Enter the values for the numerator and denominator, and then enter the value of b 1 . b = Exiyi -(Exi Zy)/D = Ex - ([xi)' The y-intercept of the least squares line is On the following scatter diagram of the blue sample points (circle symbols), use the orange line (square symbols) to plot the least squares line. Place A-Z the first orange square at the left edge of the graph (the y-intercept) and the second orange square at the value of y at the right edge of the graph. 10 O O Regression Line O s of an inch) Type here to search O Ei m W 01:56 6:10 PM ENG 6/06/2021