Question
In: Statistics and Probability
Find the regression equation using the following set of data with y as the response variable....
Find the regression equation using the following set of data with y as the response variable.
| x | y |
|---|---|
| 40.2 | 82.2 |
| 54.2 | 111.8 |
| 43 | 84.3 |
| 30.7 | 68.5 |
| 33 | 90.8 |
| 42.8 | 78.5 |
| 30.9 | 71.7 |
| 28.6 | 69.8 |
| 36.6 | 83.1 |
| 41.1 | 93.9 |
| 26.6 | 63.9 |
| 45.5 | 95.5 |
What is the correlation coefficient? use three decimal
places.
r =
What is the regression line equation. Use each value to three
decimal places.
ˆyy^ = + x
What is the predicted value of the response variable, when using a
value of 32.1 as the explanatory variable. ? Write answer accurate
to one decimal place.
ˆyy^ =
Solutions
Expert Solution
| X | Y | X * Y | X2 | Y2 | |
| 40.2 | 82.2 | 3304.44 | 1616.04 | 6756.84 | |
| 54.2 | 111.8 | 6059.56 | 2937.64 | 12499.24 | |
| 43 | 84.3 | 3624.9 | 1849 | 7106.49 | |
| 30.7 | 68.5 | 2102.95 | 942.49 | 4692.25 | |
| 33 | 90.8 | 2996.4 | 1089 | 8244.64 | |
| 42.8 | 78.5 | 3359.8 | 1831.84 | 6162.25 | |
| 30.9 | 71.7 | 2215.53 | 954.81 | 5140.89 | |
| 28.6 | 69.8 | 1996.28 | 817.96 | 4872.04 | |
| 36.6 | 83.1 | 3041.46 | 1339.56 | 6905.61 | |
| 41.1 | 93.9 | 3859.29 | 1689.21 | 8817.21 | |
| 26.6 | 63.9 | 1699.74 | 707.56 | 4083.21 | |
| 45.5 | 95.5 | 4345.25 | 2070.25 | 9120.25 | |
| Total | 453.2 | 994 | 38605.6 | 17845.36 | 84400.92 |
Part a)
r = 0.868
Equation of regression line is Ŷ = a + bX
b = 1.461
a =( Σ Y - ( b * Σ X) ) / n
a =( 994 - ( 1.4606 * 453.2 ) ) / 12
a = 27.671
Equation of regression line becomes Ŷ = 27.671 + 1.461
X
When X = 32.1
Ŷ = 27.671 + 1.461 X
Ŷ = 27.671 + ( 1.461 * 32.1 )
Ŷ = 74.6
orchestra answered 3 years agoRelated Solutions
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
15.5
58.8
25.4
62.9
53.7
68.8
46.5
78.6
28.5
57.5
5.7
68.1
-0.4
67.8
43.8
87.7
23.1
64.9
31.3
81.3
48.2
80.1
15.9
71.1
1) Find the correlation coefficient and report it accurate to
three decimal places.
r =
2) What proportion of the variation in y can be
explained by the variation in the values of x? Report
answer as...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
81
81.3
92.6
90.8
80.1
94.9
77.8
53.4
89.4
102.9
70.3
38.2
90.2
98
81.4
94.6
94.9
122.4
77.2
42.1
70.6
47.8
71
50.6
Find the correlation coefficient and report it accurate to three
decimal places.
r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
73
16.1
80
14.9
72.5
8.5
55.8
33.6
54.6
23.4
76.6
26.2
74.6
19.1
40.2
40.6
58.7
25.8
Find the correlation coefficient and report it accurate to three
decimal places.
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage accurate to one decimal place. (If the answer...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable. x y 26.1 54.3 28.4 42.5 33.8 50.2
63.4 63.3 64.3 79.4 72.5 76.1 46.2 57.4 70.2 82.1 50.5 64.3 55.4
58.8 40.7 48.5 69.4 57.5 40.4 47.8 45.1 60 64 72.5 50.6 56.9 44.2
65.6 Verify that the correlation is significant at an α = 0.05 . If
the correlation is indeed significant, predict what value (on
average) for the explanatory variable...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
58.6
56.3
66.3
72.1
54.8
119.2
57.4
83.2
62.8
74.3
77.6
72.2
71.8
62.2
46.4
77.2
77.4
86.6
60.5
78.4
66.4
131.3
76.4
113.5
68.5
84.2
81.5
102
77.5
136.3
49
12.2
Verify that the correlation is significant at an α=0.05. If the
correlation is indeed significant, predict what value (on average)
for the explanatory variable will give you a value...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable. x y 37.2 26.9 66.2 41.4 80.9 37.6
83.7 45 55 31.2 46.3 29.1 82 44.1 71.6 36.1 54.7 29.3 56.4 33.8
Predict what value (on average) for the response variable will be
obtained from a value of 45.1 as the explanatory variable. Use a
significance level of α = 0.05 to assess the strength of the linear
correlation. What is the predicted...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
62.4
39.2
62.2
40.4
47.7
68.9
120.5
-36.5
49
37.9
69.1
-9.4
53.2
71.8
66
13.8
87
8.4
92.3
-1.6
70.3
17.8
Verify that the correlation is significant at an α=0.05α=0.05.
If the correlation is indeed significant, predict what value (on
average) for the explanatory variable will give you a value of 67.7
on the response variable.
What is the predicted...
Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
6.7
-14.1
29.8
23.2
61.4
85.8
23.6
11.5
1.4
-54.8
29.5
22
54.2
30.9
35.1
7.9
23.3
13.2
29.5
6.7
27.3
29.2
18.6
-15.7
Find the correlation coefficient and report it accurate to three
decimal places.
r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
percentage...
For the following data, find the regression equation for predicting Y from X X Y 1...
For the following data, find the regression equation for
predicting Y from X
X
Y
1
2
4
7
3
5
2
1
5
8
3
7
1a.
Group of answer choices
a. Ŷ = -2X + 8
b. Ŷ =2X + 8
c. Ŷ =1.8X - 0.4
d. Ŷ =1.8X + 0.4
1b.
For the following scores, find the regression equation for
predicting Y from X
X
Y
3
8
6
4
3
5
3
5
5
3
Determine the regression equation (write the regression equation) of the following data, where Y is the...
Determine the regression equation (write the regression
equation) of the following data, where Y is the dependant variable
and X is the predictor:
X
Y
5
85
4
103
6
70
5
82
5
89
5
98
6
66
6
95
2
169
7
70
7
48
b) Interpret the regression coefficients.
c) Graph the regression line.
d) Use the regression equation to predict Y for
X=3.
e) Compute the coefficient of
determination.
f) Interpret the coefficient of
determination.
g)...
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