Question
In: Statistics and Probability
Consider the bivariate data: x : 10 , 12 , 14 , 15 , 16 y...
Consider the bivariate data:
x : 10 , 12 , 14 , 15 , 16
y : 8 , 7 , 5 , 4 , 1
Formulate the linear regression formula and estimate the value of y when x=5
Solutions
Expert Solution
Let the regression equation be given by
y=mx+c
Here, m represent slope of the regression line and c represent intercept of the regression line.
Here we need to find the value of m and c.
The value of slope is given by
The value of intercept is given by
Here the values are given
below
The linear regression equation is given by
Here, we need to find the value of y for given value of x=5
The value of y is 14.05184
The graph of the regression line is given below
orchestra answered 2 years agoRelated Solutions
Given the following data X 12 5 6 8 11 23 14 16 15 5 Y...
Given the following data
X
12
5
6
8
11
23
14
16
15
5
Y
6
10
6
5
2
4
20
5
6
10
a. Is there a linear correlation between X and Y? Explain your
answer.
b. What is the regression question?
c. If x value is 37, what is the y value?
11 12 11 10 14 15 16 12 11 10 12 20 13 32 35 14...
11
12
11
10
14
15
16
12
11
10
12
20
13
32
35
14
41
12
10
11
12
12
13
16
14
17
18
19
12
13
14
10
10
14
11
10
12
14
12
13
16
14
17
19
20
15
25
15
45
45
44
41
40
14
18
19
24
20
26
36
34
30
31
50
15
12
Find the following:
Mean? (1) Median (2), and Mode?
Find : Q3, Q1, D7,...
Consider the following data set with 10 observations: 6, 7, 7, 8, 10, 12, 14, 16,...
Consider the following data set with 10 observations: 6, 7, 7,
8, 10, 12, 14, 16, 18, X . Find 3 different values of X for which
mean=median .
Consider the following sample: x 9 6 7 5 8 y 19 14 16 12...
Consider the following sample:
x
9
6
7
5
8
y
19
14
16
12
15
Calculate the coefficient of correlation. Does correlation
coefficient provide information about the relationship between x
and y? Explain.
Find the linear regression line.
Find y, if x is 10.
Consider the following sample data: x 22 24 27 21 23 14 14 15 y 101...
Consider the following sample data:
x 22 24 27 21 23 14 14 15
y 101 139 250 88 87 14 16 20
Data is in the spreadsheet.
Use Excel's Regression tool in Data Analysis to find the sample
regression equation for the model: y = β0 + β1x + ε. What is the
coefficient for β0 ? (Enter your answer rounded to 2 decimal
places. If you got 876.36905323 for your answer, you would type
876.37)
Neck (Y) Waist (X) 13 30 14 36 12 28 14 27 15 28 15 33...
Neck (Y)
Waist (X)
13
30
14
36
12
28
14
27
15
28
15
33
16
36
13
31
16
40
13
30
14
37
13
33
14
35
12
24
14
35
15
35
17
43
14
36
13
29
13
31
* If you are able to can you please type out and number the
answers to each one so it's easier to understand. Thank you!
1) T-statistic, degree of freedom and P-value (assume
a=0.05)
2) Explain...
Neck (Y) Waist (X) 13 30 14 36 12 28 14 27 15 28 15 33...
Neck (Y)
Waist (X)
13
30
14
36
12
28
14
27
15
28
15
33
16
36
13
31
16
40
13
30
14
37
13
33
14
35
12
24
14
35
15
35
17
43
14
36
13
29
13
31
* If you are able to can you please type out and number
the answers to each one so it's easier to understand. Thank
you!
1) T-statistic, degree of freedom and P-value (assume
a=0.05)
2) Explain...
Calculate the sample covariance of the following bivariate data set. X Y 27 5 15 6...
Calculate the sample covariance of the following bivariate data
set. X Y 27 5 15 6 12 -2 b. Calculate the coefficient of
correlation of the data set. c. Describe in words the information
given to us by the sample covariance and by the sample correlation.
Explain how the correlation gives us more precise information.
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...
Consider the x, y data: x-data (explanatory variables): 10, 15, 20, 25, 30, 35, 40, 45,...
Consider the x, y data:
x-data (explanatory variables):
10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90,
95, 100
y-data (response variables):
1359.9265, 1353.3046, 220.7435, 964.6208, 1861.9920, 1195.3707,
1702.0145, 2002.0900, 1129.1860, 1864.5241, 1444.2239, 2342.5453,
2410.9056, 2766.2245, 2135.2241, 3113.7662, 4311.7260, 3313.1042,
4072.0945
Compute a best fit line to the data. Report:
a. The slope coefficient, β1:
b. The intercept coefficient, β0:
c. The standard error of the residuals
σε:
d. The Adjusted...
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