Question 1(1) Use least-squares regression to fit a straight line toX4531126y45(2) Use polynomial regression to fit a parabola to the data.(3) Compute the standard error of the estimate and the correlation coefficient of the linearmodel.1.53278810913(4) Compute the standard error of the estimate and the correlation coefficient of the linear model.(5) Plot the two-regression models in one figure.(6) Compare the results of the two regression methods.

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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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A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ŷ = 1 – 2xwhere x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way: O When amount of schooling increases by one year, the number of pregnancies increases by 2. O When amount of schooling increases by one year, the number of pregnancies decreases by 1. O When amount of schooling increases by one year, the number of pregnancies increases by 1. O When amount of schooling increases by one year, the number of pregnancies decreases by 2. Check Answer
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…
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 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 ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = 317.43 -31.272 (b) For each 1000-foot increase in elevation, how many fewer…
Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where X is the age of the crab in months and Y is the predicted value of Y, the size of the male crab in cm. Y = 8.2052 + 0.5693X What is the value of Ý when a male crab is 21.7865 months old? Provide your answer with precision to two decimal places. Interpret the value of Ý. The value of Ý is the probability that a crab will be 21.7865 months old. the predicted number of crabs out of the 1,000 crabs collected that will be 21.7865 months old. the predicted incremental increase in size for every increase in age by 21.7865 months. the predicted size of a crab when it is 21.7865 months old.
I need the right answer to d, e, and f ASAP, please.
An article gave a scatter plot along with the least squares line of x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. The accompanying values were read from the plot. x 6 12 14 20 23 30 40 50 55 67 72 79 96 112 127 y 4 10 13 15 15 25 27 46 38 46 53 74 82 99 104 (a) Does a scatter plot of the data support the use of the simple linear regression model? Yes, the scatterplot shows a reasonable linear relationship.Yes, the scatterplot shows a random scattering with no pattern. No, the scatterplot shows a reasonable linear relationship.No, the scatterplot shows a random scattering with no pattern. (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.) slope intercept (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 50. (Round your answer to four decimal places.) m3(d) Calculate a point estimate of the…
A student is preparing to take a stand allies exam she was told that she needs to get plenty of sleep the night before the exam she is interested in the relationship between the number of hours of sleep a student gets her for an exam and the score earned on the exam. She collects information from 10 other students who have already taken the exam as shown on the table. she fits at least squares regression line to the data and determines the equation of the line is why equals 26-0.18 X where why is the score earn on the exam and ask is the number of hours of sleep the night before the exam. The residual is given. based on the residual plot is the linear model appropriate? no, there is no clear pattern in the residual plot. yes, there is no clear pattern in the residual plot. no, the student who got the most you've had a negative residual yes, there are more negative residuals (6) then positive residuals (4)
A horizontal least squares regression line, implies that: Select one: a. The slope of the regression equation is 0 * b. None of the above is correct O c. The slope of the regression equation is positive d. The slope of the regression equation is negative
Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent varia (-1, 1), (1, -1), (3,-2) 2 X

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(1) Use least-squares regression to fit a straight line to X 4 5 3 4 y 1 1 2 1.5 3 2 6 5 7 8 8 10 9 13