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: 317.16 28.31 11.24 0.002 Elevation: -28.707 3.511 -8.79 0.003 S = 11.8603 R-Sq = 97.8% a) 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.) b) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? ______ % c) What percentage is unexplained?
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: 317.16 28.31 11.24 0.002
Elevation: -28.707 3.511 -8.79 0.003
S = 11.8603 R-Sq = 97.8%
a) 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.)
b) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?
______ %
c) What percentage is unexplained?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
