Question
In: Statistics and Probability
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. (For purposes of this exercise, consider a proportion large if it is at least 0.55.)
The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.
(c)
Compute the sample correlation coefficient. (Round your answer to three decimal places.)
Solutions
orchestra answered 1 year agoRelated Solutions
Consider the data. xi 3 12 6 20 14 yi 65 40 45 15 25 The...
Consider the data.
xi
3
12
6
20
14
yi
65
40
45
15
25
The estimated regression equation for these data is
ŷ = 68.25 − 2.75x.
(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 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 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 55 35 45 10 15 The...
Consider the data.
xi
3
12
6
20
14
yi
55
35
45
10
15
The estimated regression equation for these data is ŷ =
62.25 − 2.75x.
(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...
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 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.
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...
Consider the data. xi 2 6 9 13 20 yi 7 19 8 24 22 (a)...
Consider the data.
xi
2
6
9
13
20
yi
7
19
8
24
22
(a)
What is the value of the standard error of the estimate? (Round
your answer to three decimal places.)
(b)
Test for a significant relationship by using the t
test. Use α = 0.05.
State the null and alternative hypotheses.
H0: β1 ≠ 0
Ha: β1 = 0
H0: β1 ≥ 0
Ha: β1 <
0
H0: β1 = 0
Ha: β1 ≠ 0
H0:...
Consider the data. xi 2 6 9 13 20 yi 7 17 10 28 24 (a)...
Consider the data.
xi
2
6
9
13
20
yi
7
17
10
28
24
(a)
What is the value of the standard error of the estimate? (Round
your answer to three decimal places.)
_________
(b)
Test for a significant relationship by using the t
test. Use α = 0.05.
State the null and alternative hypotheses.
H0: β0 = 0
Ha: β0 ≠ 0
H0: β1 = 0
Ha: β1 ≠
0
H0: β0 ≠ 0
Ha: β0 = 0...
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