Define and discuss "least-squares criterion" giving detailed computations for finding the equation of the least squares line and the coefficient of determination. What does coefficient of determination tell you about explained variation of y in a random sample of data pairs (x, y) ?
Solution: Here concept of simple linear regression is used.
Define and discuss "least-squares criterion" giving detailed computations for finding the equation of the least squares...
we use the form y 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...
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...
Consider two variables and the least squares equation for their line y=.8565 + 0.40248 x. Regression analysis revealed the following: s = 0.517508 r = .9838 What percentage of the variation of y cannot be explained by the variation of x?
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? = 0.448 Calculate the coefficient of determination (Round to three decimal places as needed.) What does this tell you about the explained variation of the data about the regression line? % of the variation can be explained by the regression line. Round to one decimal place...
a) Obtain the equation of the least squares line.
b) Calculate the coefficient of determination.
c) Calculate an estimate of the error standard deviation
(sigma) in the simple linear regression model.
Your T For the past decade, rubber powder has been used In asphalt cement to improve performance. An article Includes a (MPa) on x - cube strength (MPa) based on the following sample data regression of y-axial strength x112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 y|...
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? r=-0.587
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? requals=0.839
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? requals=0.2910.291 Calculate the coefficient of determination. nothing (Round to three decimal places as needed.)
5. (2 points) When a least-squares linear regression equation is constructed based upon a data set, and a line is constructed from this equation, which (Gif any) of the following is a. The point (F,) must be on the regression line. b. The point (0,b) must be on the regression line. c. The point (0,b) must be on the regression line. d. None of the above statements are false. All of the above statements are true. ons for ss is...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 30 43 31 47 23 40 34 52 y 30 21 22 13 29 17 21 14 Complete parts (a) through (e), given Σx = 300, Σy = 167, Σx2 = 11,908, Σy2 = 3761, Σxy = 5885, and r ≈ −0.888. (a) Draw...