The symbol for the intercept of a least squares line is O A. b, О В. г O C. Sy O D. y O E. bo

At a university, undergraduates were asked their own height and the ideal height for their ideal spouse or partner. The table shows the data for a representative sample of 10 students, where x represents the height of the students and y represents the height for their ideal spouse or partner. All heights are in inches. Complete parts a through c. X y 59 67 61 71 66 72 73 75 69 71 X y 67 63 70 63 71 67 73 67 75 67 n a. Find the least squares line and correlation coefficient for this data. What strange phenomenon do you observe? Find the least squares line using a graphing calculator. The least squares line is Y = (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.)

We use the form  ŷ = a + bx  for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 315.27 28.31 11.24 0.002 Elevation -31.812 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.8%       Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation  ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ =   +   x (b) For each 1000-foot increase in elevation,…

We use the form  ŷ = a + bx  for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state.   A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 316.62 28.31 11.24 0.002 Elevation -30.516 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2%   The printout gives the value of the coefficient of determination r2. What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Round your answer to four decimal places.)   What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares…

2. The Mach number of a moving object is the ratio of its speedto the speed of sound. The following table shows the speeds of a jet aircraft, in terms of Mach numbers, and the time tafter it starts to accelerate. Find the least- squares line of s as a function of t. t(min) 0.00 s(Mach Number) 0.88 0.60 0.97 1.20 1.03 1.80 1.11 2.40 1.19 3.00 1.25

Please answer 1 and 2

It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 1 2 5 6 y 48 41 33 26 Find the equation of the least-squares line  = a + bx. (Round your answers to four decimal places.)   =  +  x

During oil drilling operations, components of the drilling assembly may suffer from sulfide stress cracking. An article reported on a study in which the composition of a standard grade of steel was analyzed. The following data on y = threshold stress (% SMYS) and x = yield strength (MPa) was read from a graph in the article (which also included the equation of the least squares line). X 634 643 712 709 y S = 100 92 87 83 835 78 (b) Compute the estimated standard deviation s 820 810 75 74 870 63 856 923 878 937 57 55 ΣΥ, = 10,575, ΣΥ, = 892, Σχιζ = 8,739,877, = 8,739,877, Σy? L x = 65,852, ExY, = 701,865 (a) What proportion of observed variation in stress can be attributed to the approximate linear relationship between the two variables? (Round your answer to four decimal places.) (Round your answer to four decimal places.) SB₁ 47 Does it appear that this true average change has been precisely estimated? O This is a fairly wide interval, so has been precisely estimated. 0 O This is a…

Data for motor vehicle production in a country for the years 1997 to 2004 are given in the table. Year 1997 1998 1999 2000 2001 2002 2003 2004 Thousands 1,578 1,671 1,805 2,009 2,391 3,219 4,415 5,092 (A) Find the least squares line for the data, using x = 0 for 1990. y = (Use integers or decimals for any numbers in the expression. Do not round until the final answer. Then round to the nearest tenth as needed.)

Percentages of public school students in fourth grade in 1996 and in eighth grade in 2000 who were at or above the proficient level in mathematics are given for eight western states. Find the equation of the least-squares line that summarizes the relationship between x = 1996 fourth-grade math proficiency percentage and y = 2000 eighth-grade math proficiency percentage. (Give the numerical values to four decimal places.) |4th grade 8th grade (1996) State (2000) Arizona 15 21 California 11 18 Hawaii 16 16 Montana 22 37 New Mexico 13 13 Oregon 21 32 Utah 23 26 Wyoming 19 25 n USE SALT ŷ =