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In (a)By hand, draw a scatter
Chapter 3, Problem 12AYU(choose chapter or problem)
Problem 12AYU
In Problems
(a)By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable.
(b)Select two points from the scatter diagram and find the equation of the line containing the points selected.
(c)Graph the line found in part (b) on the scatter diagram.
(d)By hand, determine the least-squares regression line.
(e)Graph the least-squares regression line on the scatter diagram.
(f )Compute the sum of the squared residuals for the line found in part (b).
(g)Compute the sum of the squared residuals for the least-squares regression line found in part (d).
(h)Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d).
x |
5 |
10 |
15 |
20 |
25 |
y |
2 |
4 |
7 |
11 |
18 |
Questions & Answers
QUESTION:
Problem 12AYU
In Problems
(a)By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable.
(b)Select two points from the scatter diagram and find the equation of the line containing the points selected.
(c)Graph the line found in part (b) on the scatter diagram.
(d)By hand, determine the least-squares regression line.
(e)Graph the least-squares regression line on the scatter diagram.
(f )Compute the sum of the squared residuals for the line found in part (b).
(g)Compute the sum of the squared residuals for the least-squares regression line found in part (d).
(h)Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d).
x |
5 |
10 |
15 |
20 |
25 |
y |
2 |
4 |
7 |
11 |
18 |
ANSWER:
Answer :
Step 1
Consider the table
x |
y |
5 |
2 |
10 |
4 |
15 |
7 |
20 |
11 |
25 |
18 |
Here x as the explanatory variable and y as the response variable.
The scatter plot is given below.
b) The two points are (5,2) and (25,18)
Here ( = (5 ,2) and (
= (25 ,18)
The slope of the line is
m =
m =
m =
m = 0.8
Therefore, Slope of the line m = 0.8
Use the slope and either of the two points to find the y-intercept.
y = mx + b
2 = 0.8 (5) + b