Consider the data points (1,2), (2,6), and (3,13). Find the straight line that provides the best least-squares fit to these data. The equation of the least-squares line is ________ (Simplify your answer. Type an equation. Type your answer in slope-intercept form.)
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Consider the data points (1,2), (2,6), and (3,13). Find the straight line that provides the best least-squares fit to these data.
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- 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…
- 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. Constant 317.97 28.31 11.24 0.002 Elevation -28.572 3.511 -8.79 0.003 S = 11.8603 R-Sq 94.2% %3D 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. %3D (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 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…Consider the following. x 1 2 3 4 y 4 6 9 13 (a) Find an equation of the least-squares line for the data. (Give each answer correct to 3 decimal places.)y = x +(b) Draw a scatter diagram for the data and graph the least-squares line.
- 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 315.81 28.31 11.24 0.002 Elevation -31.650 3.511 -8.79 0.003 S = 11.8603 R-Sq = 94.6% 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 1000-foot increase in elevation, how many fewer frost-free days…(b) Estimate the least squares linear equation for R&D Expense on Assets. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable. Complete the equation for the fitted line below. Estimated R&D Expense ($000,000) =.....+.....Assets ($000,000)We use the form ý = 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. %3D A Minitab printout provides the following information. Predictor Сoef SE Coef P Constant 315.54 28.31 11.24 0.002 Elevation -28.950 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. = 315.54 X x (b) For each 1000-foot increase in elevation, how many fewer frost-free…
- The following data is given: x -2 -1 0 1 2 y 1.5 3.2 4.5 3.4 2 Determine the coefficients a and b in the function y=a/(x2+b) that best fit the data. (Write the function in a linear form, and use linear least-squares regression to determine the value of the coefficients.) Once the coefficients are determined make a plot that shows the function and the data points.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. 4 y 48 42 33 26 A USE SALT Complete parts (a) through (e), given Ex = 15, Ey = 149, Ex² = 77, Ey² = 5833, Exy = 489, and r= -0.9106. (a) Draw a scatter diagram displaying the data. 55 Graph Layers After you add an object to the graph you 50 can use Graph Layers to view and edit its properties. Fill 45 40 35 No Solution 30 25 20 O Help WebAssign. Graphing Tool ( b) Verify the given sums Σχ, Σγ, Σχ, Σy, Σχy, and the value of the sample correlation coefficient r. (Round your value forr to four decimal places.) Σχ Ey = Ex? = Ey? = Exy = r =Interpreting technology: A biologist computed a least-squares regression line for predicting the brain weight in grams of a bird from its body weight in grams. The results are presented in the following Excel output. Coefficients Intercept 3.68952298 Body Weight 0.07800925 Part: 0 / 2 Part 1 of 2 Write the equation of the least-squares regression line. Use the full accuracy shown in the Excel output (do not round your answers). Regression line equation: y = X