Question

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 a state. A Minitab printout provides the following information. Predictor Constant Elevation 3 11.8603 SE Coef 28.31 3.511 315.46 11.24 0.002 -31.68a -8.79 0.003 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 y a + bx (a) Use the printout to write the least-squares equation (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (c) The printout gives the value of the coefficient of determination 2. What is the value of r? Be sure to give the correct sign for r based on the sign of b (d) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? Step 1 (a) Use the printout to write the least-squares equation. we want to write the least-squares equation y a + bx, using the given printout. Predictor Constant Elevation S 11.8603 Coef 315.46 -31.688 SE Coef 28.31 3.511 11.24 0.002 -8.79 0.003 Recall that a is the intercept and b is the slope of the line Since the elevation is the explanatory variable, x, the coefficient of the x-term is the slope of the line. From the printout, this corresponds to the table value in the "Elevation" row, and "Coef column. Therefore The intercept is given by the value of the constant term. There is no variable, but the Minitab printout classifies this value as a "coefficient." (Note: This may or may not coincide with your previous experience with the terms "constant" and "coefficient," but it is mathematically correct for reasons that we vwill not explore in this tutorial.) The value in the "Constant" row and "Coef column is 315.46. Therefore, a Substitute these values into the least-square equation

Answer 1

least Sauare equation let Y frast fret day s per yearina state x elevation Cn thousand of feet) 315 46-31-688 X 一1/ Elevation increased by-4000 foot ". 3 1- 33-feu) er frost , days are predictedl 0-9853 B is -ve γ is also nega rive d) gy.1%-oE-unri atio n b . Corresponding- vaYįthon in χ y can be-explained in 100-931 a 2.9% unexplcu, n ed Ucmian on 3 a= 315.46 -b 2-3). 688 у 315-46-31 , 688