Question
In: Statistics and Probability
Given are five observations for two variables, x and y. xi 1 2 3 4 5...
Given are five observations for two variables, x and
y.
| xi | 1 | 2 | 3 | 4 | 5 |
| yi | 4 | 7 | 7 | 11 | 15 |
The estimated regression equation for these data is ŷ = 1 +
2.6x.
- Compute SSE, SST, and SSR using the following equations (to 1
decimal).
SSE SST SSR - Compute the coefficient of determination r2
(to 3 decimals).
Does this least squares line provide a good fit?
- Compute the sample correlation coefficient (to 4 decimals).
Solutions
Expert Solution
The statistical software output for this problem is :
SSE = 67.6
SST = 72.8
SSR = 5.2
coefficient of determination = 0.929
Good fit
sample correlation coefficient = 0.9636
orchestra answered 2 years agoRelated Solutions
Given are five observations for two variables, x and y. xi 1 2 3 4 5...
Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
3
8
6
11
13
Round your answers to two decimal places.
a. Using the following equation:
Estimate the standard deviation of ŷ* when x = 4.
b. Using the following expression:
Develop a 95% confidence interval for the expected value of
y when x = 4.
to
c. Using the following equation:
Estimate the standard deviation of an individual value of
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1.-Given are five observations for two variables, x and y. xi 1 2 3 4 5...
1.-Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
4
7
4
10
15
(d) Develop the estimated regression equation by computing the
values of b0 and b1 using b1
=(Σ(xi − x)(yi − y))/Σ(xi −
x)2 and b0 = y −
b1x.
(e)Use the estimated regression equation to predict the value of
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Given are five observations for two variables, xi yi 1 3 2 8 3 5 4...
Given are five observations for two variables,
xi
yi
1
3
2
8
3
5
4
11
5
14
Round your answers to two decimal places.
a. Estimate the standard deviation of ŷ* when x = 4. 2
b. Develop a 95% confidence interval for the expected value of y
when x = 4.
c. Estimate the standard deviation of an individual value of y
when x = 4.
d. Develop a 95% prediction interval for y when x =...
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...
Given are five observations for two variables, x and y. x i 1 2 3 4...
Given are five observations for two variables, x and
y.
x i
1
2
3
4
5
y i
4
8
6
11
14
Round your answers to two decimal places.
a. Using the following equation:
Estimate the standard deviation of ŷ* when x = 4.
b. Using the following expression:
Develop a 95% confidence interval for the expected value of
y when x = 4.
____to____
c. Using the following equation:
Estimate the standard deviation of an individual value...
Given are five observations for two variables, x and y. x i 1 2 3 4...
Given are five observations for two variables, x and
y.
x i
1
2
3
4
5
y i
4
8
6
11
14
Round your answers to two decimal places.
a. Using the following equation:
Estimate the standard deviation of ŷ* when x =
3.
b. Using the following expression:
Develop a 95% confidence interval for the expected value of
y when x = 3.
to
c. Using the following equation:
Estimate the standard deviation of an individual value...
Given are five observations for two variables, x and y. x i 1 2 3 4...
Given are five observations for two variables, x and y. x i 1 2
3 4 5 y i 4 8 5 11 13 Round your answers to two decimal places. a.
Using the following equation: Estimate the standard deviation of ŷ*
when x = 4. b. Using the following expression: Develop a 95%
confidence interval for the expected value of y when x = 4. to c.
Using the following equation: Estimate the standard deviation of an
individual value...
Given are five observations for two variables, x and y. x i 1 2 3 4...
Given are five observations for two variables, x and
y.
x i
1
2
3
4
5
y i
4
7
5
12
13
Round your answers to two decimal places.
A)
Using the following equation:
Estimate the standard deviation of ŷ* when x = 3.
B)
Using the following expression:
Develop a 95% confidence interval for the expected value of
y when x = 3. _______to___________
C)
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