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 answer to three decimal places.) ŷ = State Arizona California Hawaii Montana New Mexico Oregon Utah Wyoming 4th grade 8th grade (1996) (2000) 17 21 13 18 18 16 24 37 15 13 32 26 25 232 23 25 21

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.) State 4th grade(1996) 8th grade(2000) Arizona 15 24 California 11 21 Hawaii 16 19 Montana 22 40 New Mexico 13 16 Oregon 21 35 Utah 23 29 Wyoming 19 28   y  =

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 Сoef SE Coef T P Constant 317.43 28.31 11.24 0.002 Elevation -31.272 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% 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 ý = a + bx. (a) Use the printout to write the least-squares equation. (b) For each 1000-foot increase in elevation, how many fewer frost-free days are…

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 318.24 28.31 11.24 0.002 Elevation -30.759 3.511 -8.79 0.003 S = 11.8603 R-Sq = 97.2%       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,…

In linear analysis, what is meant by the "best fitting" or "least squares" line? Choices: A: of all possible lines, the line with the steepest slope B. The line that minimizes the differences between the actual values of y and the predicted values of y  C. of all possible lines, the line with the flattest slope  D. the line that minimizes the differences between actual values of y and the mean value of y

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 16 19 California 12 16 Hawaii 17 14 Montana 23 35 New Mexico 14 11 Oregon 22 30 Utah 24 24 Wyoming 20 23 n USE SALT ŷ =

The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level). Stories (x) Height (y) 56 1050 29 428 26 362 40 529 60 790 22 401 38 380 110 1454 100 1127 46 700 Calculate the least squares line. Put the equation in the form of:  ŷ = a + bx.  (Round your answers to three decimal places.)ŷ =  +  x

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 316.08 28.31 11.24 0.002 Elevation -31.974 3.511 -8.79 0.003 S = 11.8603 R-Sq = 97.8%       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 =  316.08 +-31.974x For each 1000-foot increase in…

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…