Concept explainers
In Exercises
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- 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.) = + xarrow_forwardLeast squares II Consider the four points (200,1950),(400,1650), (600,1800), and (800,1600). The leastsquares line is yn = 1975 - 0.45x. Explain what “leastsquares” means, using these data as a specific example.arrow_forwardThe symbol for the intercept of a least squares line is O A. b, О В. г OC. Sy O D. y O E. boarrow_forward
- а. Complete the table. (or just write answers) Xi Yi 2 2 3 4 Totals E x; = E yi = Exf = Σχy Find SSxy, SSXX B1. x, y, and fo- Write the equation of the least squares line. b. C. d) What will be y if x=10arrow_forwardIn any scatterplot, ordinary least squares (OLS) regression finds: the intersection of two lines that produce the smallest sum of squares. one line that produces the largest sum of squares. the intersection of two lines that produces the largest sum of squares. one line that produces the smallest sum of squares.arrow_forwardPercentages 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 =arrow_forward
- You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). 2 3 12 16 26 150 36 y | 45 48 70 100 200 A USE SALT Complete parts (a) through (e), given Ex = 95, Ey = 613, Ex² 2385, Σy2 %3D = 81,729, Exy = 13,774, and r - 0.9918. (a) Draw a scatter diagram displaying the data. 210 Graph Layers 200 190 After you add an object to the graph you 180 can use Graph Layers to view and edit its 170 properties. 160 Fill 150 140 130 120 110 100 No Solution 90 80 70 60 50 40 +30 O Help 20 25 30 35 10 15 40 WebAssign. Graphing Tool (b) Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Ey = Ex² = Ey? = Exy = (c) Find x, and y. Then find the equation of the least-squares…arrow_forwardWe 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 Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations. A Minitab printout provides the following information. Predictor Constant Elevation Coef 315.00 -29.166 SE Coef 28.31 3.511 I 11.24 -8.79 P 0.002 0.003 S = 11.8603 R-Sq = 96.44 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. (c) The printout gives the value of the…arrow_forwardPercentages 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.) = State 4th grade(1996) 8th grade(2000) Arizona 15 20 California 11 17 Hawaii 16 15 Montana 22 36 New Mexico 13 12 Oregon 21 31 Utah 23 25 Wyoming 19 24arrow_forward
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