Bivariate data obtained for the paired variables x and y are shown below, in the table labeled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y = 14.87 +0.88x. In the "Calculations" table are calculations involving the observed y-values, the mean y of these values, and the values y predicted from the regression equation. Sample data Calculations 160- x y (p-)2 107.2 110.7 150- 396.0100 457.7032 2.2320 122.0 130.3 140 0.0900 70.0569 65.1249 131.5 122.1 130. 72.2500 0.0001 72.0801 142.5 129.9 120- 93.5089 107.5369 152.5 160.0 0.4900 864.3600 110- 341.1409 119.4649 Send data to Excel 110 150 130 140 150 160 Column sum: 1333.2000 Column sum: 962.4100 Column sum: 366.4388 Figure 1 Answer the following. (a) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the (Choose one) ▼, which for these data is (Choose one) ▼. (b) The variation in the sample y-values that is explained by the estimated linear relationship between x and y is given by the (Choose one) which for these data is (Choose one) ▼ (c) is the proportion of the total variation in the sample y-values that is explained by the estimated linear The value ² relationship between x and y. For these data, the value of ² is. (Round your answer to at least 2 decimal places.) X ?
Bivariate data obtained for the paired variables x and y are shown below, in the table labeled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y = 14.87 +0.88x. In the "Calculations" table are calculations involving the observed y-values, the mean y of these values, and the values y predicted from the regression equation. Sample data Calculations 160- x y (p-)2 107.2 110.7 150- 396.0100 457.7032 2.2320 122.0 130.3 140 0.0900 70.0569 65.1249 131.5 122.1 130. 72.2500 0.0001 72.0801 142.5 129.9 120- 93.5089 107.5369 152.5 160.0 0.4900 864.3600 110- 341.1409 119.4649 Send data to Excel 110 150 130 140 150 160 Column sum: 1333.2000 Column sum: 962.4100 Column sum: 366.4388 Figure 1 Answer the following. (a) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the (Choose one) ▼, which for these data is (Choose one) ▼. (b) The variation in the sample y-values that is explained by the estimated linear relationship between x and y is given by the (Choose one) which for these data is (Choose one) ▼ (c) is the proportion of the total variation in the sample y-values that is explained by the estimated linear The value ² relationship between x and y. For these data, the value of ² is. (Round your answer to at least 2 decimal places.) X ?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:(Choose one)
regression sum of squares
total sum of squares
error sum of squares
(Choose one)
366.4388
962.4100
1333.2000
PhotoGrid
Transcribed Image Text:Bivariate data obtained for the paired variables x and y are shown below, in the table labeled "Sample data." These data are plotted in the scatter plot in Figure
1, which also displays the least-squares regression line for the data. The equation for this line is y = 14.87+0.88x.
In the "Calculations" table are calculations involving the observed y-values, the mean y of these values, and the values y predicted from the regression
equation.
Sample data
Calculations
160+
x
y
(x-1)²
(-5)²
(v-^^)²
150+
107.2 110.7
396.0100
457.7032
2.2320
122.0 130.3
140-
0.0900
70.0569
65.1249
131.5 122.1
130-
72.2500
0.0001
72.0801
142.5 129.9
120.
0.4900
93.5089
107.5369
152.5 160.0
110-
864.3600
341.1409
119.4649
Send data to Excel
LL
130 130 140 150 160
Column sum:
1333.2000
Column sum:
962.4100
Column sum:
366.4388
Figure 1
Answer the following.
(a)
The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best
fits" is used because the line has an equation that minimizes the (Choose one)
▼, which for these
data is (Choose one) ▼.
(b)
The variation in the sample y-values that is explained by the estimated linear relationship between x and y is given
by the (Choose one)
which for these data is (Choose one) ▼
₂2
(c)
The value is the proportion of the total variation in the sample y-values that is explained by the estimated linear
relationship between x and y. For these data, the value of ² is. (Round your answer to at least 2 decimal
places.)
110
X
?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman