Question
In: Statistics and Probability
Given are data for two variables, x and y. xi 6 11 15 18 20 yi...
Given are data for two variables, x and y.
xi 6 11 15 18 20
yi 6 8 12 20 30
Use the facts that ̄x= 14, ̄y= 15.2, ˆy=−7.02 + 1.59x, Σ(xi − ̄x)^2 = 126, and s= 4.88.
a. Compute the residuals.
b. Plot the residuals against x. Do the assumptions about the error terms seem to be satisfied?
c. Compute the standardized residuals.
Solutions
Expert Solution
b):
There present a pattern in Residuals plot which is parabola. it's means there heteroscedasticity present or we can say variance are not equal.
c):
First Calculate the Standard deviation of Residuals.
Standard deviation of Residuals:
orchestra answered 1 year agoRelated Solutions
Given are data for two variables, x and y. xi 6 11 15 18 20 yi...
Given are data for two variables, x and y.
xi
6
11
15
18
20
yi
7
7
13
21
30
(a)
Develop an estimated regression equation for these data. (Round
your numerical values to two decimal places.)
ŷ =
(b)Compute the residuals. (Round your answers to two decimal
places.)
xi
yi
Residuals
6
7
11
7
15
13
18
21
20
30
(c)Develop a plot of the residuals against the independent
variable x.
a) A residual plot has 5...
Given are data for two variables, x and y. xi 6 11 15 18 20 yi...
Given are data for two variables, x and y.
xi
6
11
15
18
20
yi
5
9
12
19
30
(a) Develop an estimated regression equation for these data.
(Round your numerical values to two decimal places.)
ŷ =
(b) Compute the residuals. (Round your answers to two decimal
places.)
xi
yi
Residuals
6
5
11
9
15
12
18
19
20
30
(d) Compute the standardized residuals. (Round your answers to
two decimal places.)
xi
yi
Standardized
Residuals...
Given are data for two variables, x and y. xi 6 11 15 18 20 yi...
Given are data for two variables, x and y.
xi
6
11
15
18
20
yi
5
9
12
21
30
(a)
Develop an estimated regression equation for these data. (Round
your numerical values to two decimal places.)
ŷ =
1.66x−7.82
(b)
Compute the residuals. (Round your answers to two decimal
places.)
xi
yi
Residuals
6
5
11
9
15
12
18
21
20
30
(c)
Develop a plot of the residuals against the independent variable
x.
A residual plot...
Given are five observations for two variables, x and y. xi 1 4 11 15 20...
Given are five observations for two variables,
x and y.
xi
1
4
11
15
20
yi
52
57
48
16
10
a. Compute SSE,
SST, and SSR.
SSE [ ] (to 2
decimals)
SST [ ] (to 2
decimals)
SSR [ ] (to 2
decimals)
b. Compute the coefficient of determination
r2. Comment on the goodness of
fit.
[ ] (to 3 decimals)
The least squares line provided an [good,bad] fit;
[ ]% of the variability in
y has...
The data is given as follow. xi 2 6 9 13 20 yi 7 18 9...
The data is given as follow.
xi
2
6
9
13
20
yi
7
18
9
26
23
The estimated regression equation for these data is =
7.6 + .9x.
Compute SSE, SST, and SSR (to 1 decimal).
SSE
SST
SSR
What percentage of the total sum of squares can be accounted for by
the estimated regression equation (to 1 decimal)?
%
What is the value of the sample correlation coefficient (to 3
decimals)?
Student ID: Question 1 Given are five observations for two variables, x and y. xi yi...
Student ID: Question 1 Given are five observations for two
variables, x and y. xi yi 2 25 3 25 5 20 1 30 8 16 a. Develop the
regression equation by computing the values of βˆ 0 and βˆ 1. b.
Use the estimated regression equation to predict the value of y
when x = 6. c. Compute SSE, SST, and SSR. d. Compute the
coefficient of determination r 2 . Comment on the goodness of fit.
e. Compute...
Consider the data. xi 3 12 6 20 14 yi 60 35 55 15 15 The...
Consider the data.
xi
3
12
6
20
14
yi
60
35
55
15
15
The estimated regression equation for these data is
ŷ = 69 − 3x.
(a) :
Compute SSE, SST, and SSR using equations
SSE = Σ(yi −
ŷi)2, SST =
Σ(yi −
y)2, and SSR =
Σ(ŷi −
y)2.
SSE=
SST=
SSR=
(b)
Compute the coefficient of determination
r2 (Round your answer to three decimal
places.)
r2 =
Comment on the goodness of fit. (For purposes...
Consider the data. xi 3 12 6 20 14 yi 65 40 60 15 20 The...
Consider the data.
xi
3
12
6
20
14
yi
65
40
60
15
20
The estimated regression equation for these data is
ŷ = 75.75 − 3.25x.
(a)
Compute SSE, SST, and SSR using equations
SSE = Σ(yi −
ŷi)2,
SST = Σ(yi −
y)2,
and
SSR = Σ(ŷi −
y)2.
SSE = SST = SSR =
(b)
Compute the coefficient of determination
r2.
(Round your answer to three decimal places.)
r2
=
Comment on the goodness of fit....
Consider the data. xi 3 12 6 20 14 yi 65 35 50 15 20 The...
Consider the data.
xi
3
12
6
20
14
yi
65
35
50
15
20
The estimated regression equation for these data is
ŷ = 70 − 3x.
(a)
Compute SSE, SST, and SSR using equations
SSE = Σ(yi −
ŷi)2,
SST = Σ(yi −
y)2,
and
SSR = Σ(ŷi −
y)2.
SSE=SST=SSR=
(b)
Compute the coefficient of determination
r2.
(Round your answer to three decimal places.)
r2
=
Comment on the goodness of fit. (For purposes of this exercise,...
Consider the following data for two variables, x and y. x 9 32 18 15 26...
Consider the following data for two variables, x and
y.
x
9
32
18
15
26
y
10
19
22
17
23
(a) Develop an estimated regression equation for the data of the
form ŷ = b0 +
b1x. (Round
b0 to two decimal places and
b1 to three decimal places.)
ŷ =
Comment on the adequacy of this equation for predicting
y. (Use α = 0.05.)
The high p-value and low coefficient of determination
indicate that the equation is...
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