Question
In: Statistics and Probability
Given the following values of income and consumption x 20 11 15 10 17 19 y...
Given the following values of income and consumption
| x | 20 | 11 | 15 | 10 | 17 | 19 | |
| y | 5 | 15 | 14 | 17 | 8 | 9 |
a) Find the covariance
b) Find and explain the correlation
c) Determine the equation of least squares line
d) Find predicted values of Y for X = 16 & 25
Solutions
Expert Solution
from the table we calculate the
mean and the sum of squares
let "m" be the slow and "n" be
the Y intercept
orchestra answered 2 years agoRelated Solutions
Given the following numbers: 25 16 61 18 15 20 15 20 24 17 19 28,...
Given the following numbers: 25 16 61 18 15 20 15 20
24 17 19 28, derive the mean, median, mode, variance, standard
deviation, skewness, kurtosis, range, minimum, maximum, sum, and
count. Interpret your results. What is the empirical rule for two
standard deviations of the data?
Given the following numbers: 25 16 61 18 15 20 15 20 24 17 19 28,...
Given the following numbers: 25 16 61 18 15 20 15 20 24 17 19
28, derive the mean, median, mode, variance, standard deviation,
skewness, kurtosis, range, minimum, maximum, sum, and count.
Interpret your results. What is the empirical rule for two standard
deviations of the data?
Given the following five pairs of (x, y) values, x 1 3 11 8 14 y...
Given the following five pairs of (x, y)
values,
x
1
3
11
8
14
y
10
7
4
2
1
(a)
Determine the least squares regression line.
(Be sure to save your unrounded values of b0
and b1 for use in Problem #6 below.)
(b)
Draw the least squares regression line accurately on a
scatterplot. Then look to see which (x, y) pairs
are above the regression line. Then add up the
y-values for all of the (x, y)...
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 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 following data for two variables, x and y. x 10 34 20 11 24...
Consider the following data for two variables, x and y.
x
10
34
20
11
24
y
11
30
22
19
21
a. Develop an estimated regression equation for
the data of the form y=b0+b1x. Comment on the
adequacy of this equation for predicting . Enter negative value as
negative number.
The regression equation is
Y=___________+___________ (to 2 decimals)
s=__________ (to 3 decimals)
r2=_________% (to 1 decimal)
r2 adj=_______ % (to 1 decimal)
Analysis of Variance
SOURCE
DF
SS
(to...
Find dy/dx by implicit differentiation. 11. ycosx=x^2+y^2 13. sqrt(x+y)=x^4+y^4 15. tan(x/y)=x+y 17. sqrt(xy)=1+(x^2)*(y) 19. sin(xy) =...
Find dy/dx by implicit differentiation.
11. ycosx=x^2+y^2
13. sqrt(x+y)=x^4+y^4
15. tan(x/y)=x+y
17. sqrt(xy)=1+(x^2)*(y)
19. sin(xy) = cos(x+y)
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