Question
In: Statistics and Probability
Five observations taken for two variables follow.X= 6 10 15 20 27 Y= 6 10 6 ...
Five observations taken for two variables follow.X= 6 10 15 20 27 Y= 6 10 6 18 12 a. What does the scatter diagram indicate about a relationship between and ? b. Compute the sample covariance (to 2 decimal). c Compute the sample correlation coefficient (to 3 decimals). What can you conclude, based on your computation of the sample correlation coefficient?
Solutions
Expert Solution
By plotting the X on x axis and
Y on y axis we get this scatter plot . Which shows that there is a
positive relationship between X and Y . the relationship is good
but not extremely strong .
Then the correlation coefficient between X and Y is
r = 0.6002
So clearly r is positive. That means there is positive association between X and Y . And as r is greater than 0.5 but less than 0.8 we can say there is moderate relationship between them .
orchestra answered 1 year agoRelated Solutions
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, and . 3 6 12 17 20 59 54 47...
Given are five observations for two variables, and
.
3
6
12
17
20
59
54
47
14
16
The estimated regression equation for these data is y = 70.84 -
2.83x
a. Compute SST, SSE , and SSR.
(to 2 decimals)
(to 2 decimals)
(to 2 decimals)
b. Compute the coefficient of determination
r^2. Comment on the goodness of fit.
(to 3 decimals)
The least squares line provided an - Select your answer
-goodbadItem 5 fit; of the variability
in has been...
Given are five observations for two variables, x and y. The estimated regression equation for these...
Given are five observations for two variables, x and y. The
estimated regression equation for these data is y = 1 + 2.4x
(A) Compute SSE, SST, and SSR
(B) Compute the coefficient of determination, R^2.
(C) Compute the sample correlation coefficient.
x
y
1
3
2
8
3
5
4
12
5
13
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...
Given are five observations for two variables, x and y. (Round your answers to two decimal...
Given are five observations for two variables, x and y. (Round
your answers to two decimal places.) xi 1 2 3 4 5 yi 3 8 6 11 14
(a) Use sŷ* = s 1 n + (x* − x)2 Σ(xi − x)2 to estimate the standard
deviation of ŷ* when x = 3. Incorrect: Your answer is incorrect.
(b) Use ŷ* ± tα/2sŷ* to develop a 95% confidence interval for the
expected value of y when x = 3....
Given are five observations for two variables, x and y. (Round your answers to two decimal...
Given are five observations for two variables, x and
y. (Round your answers to two decimal places.)
xi
3
12
6
20
14
yi
55
40
55
10
15
(a)
Estimate the standard deviation of
ŷ*
when
x = 10.
(b)
Develop a 95% confidence interval for the expected value of
y when
x = 10.
to
(c)
Estimate the standard deviation of an individual value of
y when
x = 10.
(d)
Develop a 95% prediction interval for y...
Given are five observations for two variables, x and y. (Round your answers to two decimal...
Given are five observations for two variables, x and
y. (Round your answers to two decimal places.)
xi
3
12
6
20
14
yi
55
40
55
10
15
(a)
Estimate the standard deviation of
ŷ*
when
x = 10.
(b)
Develop a 95% confidence interval for the expected value of
y when
x = 10.
to
(c)
Estimate the standard deviation of an individual value of
y when
x = 10.
(d)
Develop a 95% prediction interval for y...
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