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Consider the following data:
Fit a line, y = x1 + x2t, to the data using the least squares approach.
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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 = 2 – 3xwhere 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: %3D O When amount of schooling increases by one year, the number of pregnancies decreases by 2. 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 3. O When amount of schooling increases by one year, the number of pregnancies increases by 3.The following data are the average annual repair cost (in O.R.) and the age of automobiles ( in years). Car age (x) 1 2 3 4 5 Repair Cost (y) 100 150 320 350 380 Find the equation of Y on X by least-squares regression method.let W = {x €R3 , 1 such that Ax 2 where A is any 2×3 matrix is a subspace of R³ Select one: True False
- 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 - 5xwhere 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 1. When amount of schooling increases by one year, the number of pregnancies decreases by 1. When amount of schooling increases by one year, the number of pregnancies decreases by 5. When amount of schooling increases by one year, the number of pregnancies increases by 5.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 AnswerA 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: i = 2 – 5z where 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 tends to decrease by 5. O When amount of schooling increases by one year, the number of pregnancies tends to increase by 5. O When amount of schooling increases by one year, the number of pregnancies tends to decrease by ns 2. O When amount of schooling increases by one year, the number of pregnancies tends to increase by 2. urse Submit Question math.com/assess2/3/skip/10 here to search R
- 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,…Report the equation of the regression line and interpret it in the context of the problemWe 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…
- 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: ý = 2-5z where 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 tends to decrease by 5. O When amount of schooling increases by one year, the number of pregnancies tends to increase by 5. ns O When amount of schooling increases by one year, the number of pregnancies tends to decrease by 2. re O When amount of schooling increases by one year, the number of pregnancies tends to increase by 2. urse Submit Question here to search 立Table 7 gives the number of visitors per year at YosemiteNational Park.(a) Find the least-squares line for these data.(b) Estimate the number of visitors in 2017.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…
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