We use the form ŷ = a + bx for the least-squares line. In some computer...
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 | 316.89 | 28.31 | 11.24 | 0.002 |
| Elevation | -30.435 | 3.511 | -8.79 | 0.003 |
| S = 11.8603 | R-Sq = 96.0% |
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) 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?
Homework Answers
Solution :
From given output,
(a)
The value of the coefficient of determination r 2 = 0.9600
Value of r = -0.9798 (minus sign because slope is negative)
(b)
Explained variation = 96%
(c)
Unexplained variation = 4%
Add Answer to:
We use the form ŷ = a +
bx for the least-squares line. In some computer...
We use the form y a + bx for the least-squares line. In some computer printouts, the least-square...
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 = a + bx for the least-squares line. In some computer printouts, the...
We use the form = 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 Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of...
u LLS FRUICHUISJ and 6 use the following information. Prehistoric pottery vessels are usually found as...
u LLS FRUICHUISJ and 6 use the following information. Prehistoric pottery vessels are usually found as sherds (broken pieces) and are care- fully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A.J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an...
Least Squares Linear Regression of Rent Predictor Variables Constant Size Coefficient 1276.56 0.16486 Std Error 454.843...
Least Squares Linear Regression of Rent Predictor Variables Constant Size Coefficient 1276.56 0.16486 Std Error 454.843 0.41717 T 2.81 0.40 P 0.0072 0.6945 Mean Square Error (MSE) Standard Deviation 458532 677.150 R2 Adjusted R2 AICC PRESS 0.0032 -0.0175 656.27 2.34E+07 DF F 0.16 P 0.6945 1 Source Regression Residual Total MS 71610.6 458532 SS 71610.6 2.201E+07 2.208E+07 48 49 20.14 0.0006 Lack of Fit Pure Error 42 6 2.185E+07 155000 520346 25833.3 Cases Included 50 Missing Cases 0 7. Identify...
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x...
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...
It is thought that prehistoric Indians did not take their best tools, pottery, and household items...
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a...
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 29 44 33 47 23 40 34 52...
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 29 44 33 47 23 40 34 52 y 32 20 26 13 29 17 21 14 Complete parts (a) through (e), given Σx = 302, Σy = 172, Σx2 = 12,064, Σy2 = 4036, Σxy = 6066, and r ≈ −0.902. (a) Draw...
(10 points) The following regression output is available. Notice that some of the values are missing....
(10 points) The following regression output is
available. Notice that some of the values are missing.
Predictor Coef SE
Coef T P
Constant 5.932 2.558 2.320 0.068
x 0.511 6.083 0.001
Analysis of Variance
Source DF SS MS F P
Regression 648.72 648.72 57.20 0.001
Residual
Error 56.70
Total 16 705.43
Based on the information given, what is the value of sum of
squares of the X’s (SSxx)?
7626.92
23.142
535.591
None of the above
1. (10 points) Consider the following partially completed computer printout for a regression analysis Based on the information provided, which of the following statements is true at a...
5. (2 points) When a least-squares linear regression equation is constructed based upon a data set,...
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...
It is thought that basketball teams that make too many fouls in a game tend to...
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. х 33 26 y48 44 14, Ey 151, x2 = 66, Ey2 = 6005, Exy Complete parts (a) through (e), given...
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...
u LLS FRUICHUISJ and 6 use the following information. Prehistoric pottery vessels are usually found as sherds (broken pieces) and are care- fully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A.J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an...
Least Squares Linear Regression of Rent Predictor Variables Constant Size Coefficient 1276.56 0.16486 Std Error 454.843 0.41717 T 2.81 0.40 P 0.0072 0.6945 Mean Square Error (MSE) Standard Deviation 458532 677.150 R2 Adjusted R2 AICC PRESS 0.0032 -0.0175 656.27 2.34E+07 DF F 0.16 P 0.6945 1 Source Regression Residual Total MS 71610.6 458532 SS 71610.6 2.201E+07 2.208E+07 48 49 20.14 0.0006 Lack of Fit Pure Error 42 6 2.185E+07 155000 520346 25833.3 Cases Included 50 Missing Cases 0 7. Identify...
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a...
(10 points) The following regression output is
available. Notice that some of the values are missing.
Predictor Coef SE
Coef T P
Constant 5.932 2.558 2.320 0.068
x 0.511 6.083 0.001
Analysis of Variance
Source DF SS MS F P
Regression 648.72 648.72 57.20 0.001
Residual
Error 56.70
Total 16 705.43
Based on the information given, what is the value of sum of
squares of the X’s (SSxx)?
7626.92
23.142
535.591
None of the above
1. (10 points) Consider the following partially completed computer printout for a regression analysis Based on the information provided, which of the following statements is true at a...
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...
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. х 33 26 y48 44 14, Ey 151, x2 = 66, Ey2 = 6005, Exy Complete parts (a) through (e), given...
Most questions answered within 3 hours.
-
D. A student completed 20 courses in the School of Arts and
Sciences. Her grades in...
asked 1 hour ago -
teo
pucks moving on a frictionless air table are about to collide. the
1.5 kg puck...
asked 1 hour ago -
Problem #1
The area between Z = 0 and Z = 2.50
The area between Z...
asked 3 hours ago -
1. What is the meaning of the term communication style?
2. What are the benefits to...
asked 2 hours ago -
9.) You are buying a car that cost $26,500. You make payments of
$412 each month...
asked 2 hours ago -
. Suppose a discrete random variable has probability
distribution
P(x) = .2 if x = 0...
asked 4 hours ago -
Under the influence of its drive force, a snowmobile is moving
at a constant velocity along...
asked 4 hours ago -
Why do organizations decline? What steps can top
management take to halt, decline, and restore organizational...
asked 4 hours ago -
What mechanisms Drive speciation??
(I.e. what was Dawins theory on the orgin of species, and how...
asked 5 hours ago -
The manager at a car assembly plant believes that the mean
assembly time for a car...
asked 6 hours ago -
Which of the following is true of electron capture?
A) It decreases the nuclide's mass number...
asked 8 hours ago -
Assuming an efficiency of 43.10%, calculate the actual yield of
magnesium nitrate formed from 114.9 g...
asked 8 hours ago