Answered: t-slope form to fi

Math

Statistics

t-slope form to fi

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The proiessur of an introductory statistics course has found something interesting: there may be a relationship between scores on his first midterm and the number of years the test-takers have spent at the university. For the 64 students taking the course, the professor found that the least-squares regression Español equation relating the two variables number of years spent by the student at the university (denoted by x) and score on the first midterm (denoted by y) is y = 82.52- 2.53x. The standard error of the slope of the least-squares regression line is approximately 1.55. %3D Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope B,: (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 level of significance, and perform a two- tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) Aa…
A motorist found that the efficiency of her engine could be increased by adding lubricating oil to fuel. She experimented with different amounts of lubricating oil and the data are Amount of lubricating oil (ml) | 0 25 50 75 100 Efficiency (%) 60 70 75 81 84 (a) Obtain the least squares fit of a straight line to the amount of lubricating oil. (b) Test whether or not the slope B1 = 0. Take a significance. 0.05 as your level of (c) Construct a 90% confidence interval on the mean response at ro = 10 ml.
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 PConstant 317.70 28.31 11.22 0.0015Elevation −31.8123.511 −9.060.0028s = 11.8603, R-Sq = 96.5%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 = (b)For each 1,000-foot increase in elevation, how many…
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 -31.353 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.0% 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, how…
The average remaining lifetimes for women of various ages in a certain country are given in the following table. + (A graphing calculator is recommended.) (a) Find the equation of the least-squares line for the data. (Round all numerical values to two decimal places.) y= ? (b) Use the equation from part (a) to estimate the remaining lifetime (in years) of a woman of age 23. (Round your answer to the nearest year.) ? yr
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…
Consider the following. (-8, 0) y = -5 y 6 4 (0, 2) (a) Find the least squares regression line. 5 (8,6) (b) Calculate S, the sum of the squared errors. Use the regression capabilities of a graphing utility to verify your results.
When the predicted overnight temperature is between 15°F and 32°F, roads in northern cities are salted to keep water from freezing on the roadways. Suppose that a small city was trying to determine the average amount of salt y (in tons) needed per night at temperature x. They found the following least squares prediction equation: y = 20,000 - 2,500x Interpet the slope. a) 2,500 tons is the decrease in the amount of salt needed for a 1 degree increase in temperature. b) 2,500 tons is the increase in the amount of salt needed for a 1 degree increase in temperature. c) 20,000 is the increase in the amount of salt needed for a 1 degree increase in temperature. d) 2,500 tons is the expected amount of salt needed when the temperatures is 0° C.
Which of the following best describes the least-squares line fit to the data shown in the plot? (i) bo = 0, bị =-1 (ii) bo = -3, b₁ = 1 (iii) bo-5, b₁ = 2 (iv) bo = −3, bị =-1 (v) bo = 0, b₁ = -3 2 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…