Question
In: Statistics and Probability
Consider the following small data set. Subject x y 1 7 21 2 17 15 3...
Consider the following small data set.
| Subject | x | y |
| 1 | 7 | 21 |
| 2 | 17 | 15 |
| 3 | 15 | 24 |
| 4 | 5 | 19 |
| 5 | 14 | 30 |
Find the linear correlation coefficient.
?=
Given the following data set, let ? be the explanatory variable and ? be the response variable.
| x | 7 | 6 | 3 | 8 | 2 | 5 | 3 |
| y | 3 | 6 | 7 | 2 | 8 | 5 | 8 |
(a) If a least squares line was fitted to this data, what
percentage of the variation in the ? would be explained by the
regression line? (Enter your answer as a percent.)
ANSWER: %
(b) Compute the correlation coefficient: ?=
Solutions
Expert Solution
1)
| correlation r='Sxy/(√Sxx*Syy) = | 0.1061 | |
(please take care of number of decimal places)
2)
a)
| SST=Syy= | 33.714286 | |
| SSE =Syy-(Sxy)2/Sxx= | 3.708333 | |
| SSR =(Sxy)2/Sxx = | 30.005952 | |
| Coefficient of determination R2=SSR/SST=0.8900 |
percentage of the variation in the ? would be explained by the regression line =89.0 %
b)
| correlation r='Sxy/(√Sxx*Syy) = | -0.9434 | |
orchestra answered 1 year agoRelated Solutions
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443
Consider the data set:
8 4 3 6 17 15 13 7 21 11 32 1 1.
1.What is the percentile rank of xi = 21?
2. What is the value corresponding to the 61th percentile,
P61?
3. Find outliers, if exist.
Step 2 Data Set A x 1 2 3 4 5 6 7 y 7 7...
Step 2
Data Set A
x
1
2
3
4
5
6
7
y
7
7
7
9
9
9
10
Data Set B
x
1
2
3
4
5
6
7
8
9
10
11
y
4
6
6
6
8
9
9
9
10
10
10
Step 2
Find the equation for the least-squares line, and graph the
line on the scatter plot.
Find the sample correlation coefficient r and the
coefficient of determination r2. Is r
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Consider the following set of ordered pairs. x 5 2 2 3 7 6 y 3...
Consider the following set of ordered pairs. x 5 2 2 3 7 6 y 3 8 5
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alternative hypotheses. Upper H 0: beta ▼ not equals less than
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3. Consider the following data for two variables, x and y. x 2 3 4 5 7...
3. Consider the following data for two variables, x and y.
x 2 3 4 5 7 7 7 8 9
y 4 5 4 6 4 6 9 5 11
a. Does there appear to be a linear relationship between x and
y? Explain.
b. Develop the estimated regression equation relating x and
y.
c. Plot the standardized residuals versus yˆ for the estimated
regression equation developed in part (b). Do the model assumptions
appear to be satisfied? Explain.
d....
Consider the following data set. x 1 2 3 4 5 6 y 3.00 0.21 0.61...
Consider the following data set.
x
1
2
3
4
5
6
y
3.00
0.21
0.61
0.70
1.13
1.17
a) plot the data (y versus x). Are there any points that appear
to be outliers? If there are, circle them and label as such.
b) produce a regression of y against x. Add the regression line
to the plot in a). Do you think that the regression line captures
the most important features of the data set reasonably well?
c)...
Determine the vertex, focus, and directrix for the following parabola. A. y=4(x+2)^2-21 B. y-7=1/8(x-3)^2 C. x=1/4y^2
Determine the vertex, focus, and directrix for the following
parabola.
A. y=4(x+2)^2-21
B. y-7=1/8(x-3)^2
C. x=1/4y^2
A set of data has the following coordinates t 0 1 3 4 7 y 2...
A set of data has the following coordinates
t
0
1
3
4
7
y
2
4
5
7
10
a) Find the least-squares fit to this data by a linear function
of t (that is, find constants c1,c0 so that y(t) = c1t + c0 is the
best linear fit to this set of data).
b) Find the equation of the best quadratic fit to the same set
of data. Then find the equation of the polynomial of smallest...
For the data set 1 2 3 4 7 7 7 8 11 12 12 15...
For the data set
1
2
3
4
7
7
7
8
11
12
12
15
15
16
17
17
17
18
20
20
22
24
24
25
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26
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26
27
30
32
32
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36
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51
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58
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59
61
63
65
65
67
69
70
73
75
75
76
77
77
79
80
81
82
82
(a)...
2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6,...
2. Consider the following data:
x= 1, 2, 3, 4, 5
y =3, 2, 4, 6, 5
By hand, not using Matlab, and showing your work:
(a) Compute the correlation coefficient.
(b) Find the least-squares line.
(c) Find the standard deviation around the least-squares
line.
For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2,...
For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2, 4,
3, 5, 3, 7] please compute the following
1. measures of central tendency (3 points)
2. standard deviation ( 5 points)
3. is 18 an outlier? (5 points)
4. describe the shape of the distribution (2 points)
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